I just checked and a quad turret of 33% gauss you need a crew of 13, whereas two twin gauss turrets at 33% would be 14 crew, so pretty small savings.

I tweaked the design and came up with the following based on all of the recommendations so far. Note that the turrets are slightly overbuilt in terms of tracking speed, as I'm expecting a racial tracking speed update in the next two years which will allow me to upgrade the BFCs in a later retrofit. I did add a 100 ton crew compartment for RP... any ship worth it's salt should have a marine contingent. I picked a drop pod, so it may actually come in handy fending off boarders or boarding enemy ships during the post-battle mop up.

Courser class Destroyer (P)      14,991 tons       483 Crew       3,670.4 BP       TCS 300    TH 2,500    EM 3,570
8338 km/s      Armour 5-54       Shields 119-476       HTK 113      Sensors 7/0/0/0      DCR 31      PPV 79.75
Maint Life 2.26 Years     MSP 1,683    AFR 163%    IFR 2.3%    1YR 447    5YR 6,701    Max Repair 625 MSP
Troop Capacity 100 tons     Boarding Capable   
Captain    Control Rating 3   BRG   AUX   CIC   
Intended Deployment Time: 18 months    Morale Check Required   

Internal Fusion Drive  EP1250.00 (2)    Power 2500    Fuel Use 31.25%    Signature 1250    Explosion 12%
Fuel Capacity 500,000 Litres    Range 19.2 billion km (26 days at full power)
Epsilon S119 / R476 Shields (1)     Recharge Time 476 seconds (0.3 per second)

45cm Spinal Laser (1)    Range 384,000km     TS: 8,338 km/s     Power 53-5     RM 50,000 km    ROF 55       
20cm C5 Far Ultraviolet Laser (6)    Range 384,000km     TS: 8,338 km/s     Power 10-5     RM 50,000 km    ROF 10       
.33 Gage Twin PD Turret (5x10)    Range 30,000km     TS: 25000 km/s     Power 0-0     RM 30,000 km    ROF 5       
BFC R96-TS20000 (50%) (1)     Max Range: 96,000 km   TS: 20,000 km/s     90 79 69 58 48 38 27 17 6 0
BFC R384-TS10000 (70%) (1)     Max Range: 384,000 km   TS: 10,000 km/s     97 95 92 90 87 84 82 79 77 74
Tokamak Fusion Reactor R36-PB20 (1)     Total Power Output 35.7    Exp 10%

Active Search Sensor AS9-R1 (1)     GPS 21     Range 9.7m km    MCR 870.6k km    Resolution 1
Thermal Sensor TH0.5-7.0 (1)     Sensitivity 7     Detect Sig Strength 1000:  20.9m km

ECCM-1 (1)         ECM 20

This design is classed as a Military Vessel for maintenance purposes
This design is classed as a c for auto-assignment purposes

The overall designs seem reasonable. However, I candidly wonder why bother with two different classes? Both ships have considerable overlap in capabilities already, sharing the spinal laser, one 20 cm laser, and 2x Gauss turrets with the difference being between 5x lasers or 3x turrets plus associated necessities. IMO, it makes more sense on a strategic level to just build a single hybrid class with, say, spinal + 4x 20 cm lasers + 3x Gauss turrets (or thereabouts, to taste). The major reason for this is to gain resilience for your fleet so that if an enemy preferentially targets and destroys one class over the other you retain a good balance of capabilities... one of the understated dangers of naval combat is even when you win battles, say against NPRs, quite handily, you still lose a few ships by poor luck or attrition, and if you for example lose all of your main PD ships you can suddenly find yourself vulnerable to missile attacks that previously were no threat. In practice of course a navy needs multiple ship classes because (1) it is more interesting, but (2) some degree of specialization is inevitable and necessary, but in this case there is not enough difference in specialization between the two classes to really justify having two classes instead of one...IMO of course.

Specific things:

• For the weapon loadouts here I would probably not use the SW BFC for the Gauss turrets. One PD fire control and one for the main battery is sufficient for redundancy, since in an emergency each fire control can act as a backup for the other. A bit more redundancy might be ideal but for 15k ton ships using fairly large weapons space is too precious to have a lot of extra BFCs. Note that on the Yin you have 5x SW BFCs where a single MW BFC would do the job and save 60% of the tonnage.
• Personally the maint life is too close to the deployment time for my comfort level, maintenance failures can be very random so a bigger buffer is safer during extended deployments.
• For the Gauss turrets, I would strongly recommend using twin or ideally single turrets over quad particularly for full-size Gauss cannons. The reason is that while a single BFC can target multiple missile salvos per increment, a weapon can only fire at one salvo and a quad turret is counted as a single weapon for this purpose. With 20x full-accuracy shots, it is likely that your turrets will frequently overkill a salvo thus wasting many shots that could have been fired at a different salvo. With single-mount turrets much of this problem is avoided.
• The armor/shielding balance is okay, the shields are excellent but I would say the armor is if anything a bit too strong. You might see better combat performance from 4-5 layers of armor. However given that you are at IntCF tech level, weapons may be more powerful so you are probably fine. No major issues here.
• The speed is fine for the tech level. You could probably be more efficient with smaller, higher-boost engines and more fuel but personally I would err on the side of minimizing fuel consumption to make logistics easier. If you optimized the propulsion (3:1 ratio of engines to fuel) you might be able to fit another laser cannon or Gauss turret, since the 10:1 ratio you have is less efficient and takes a few % more of your tonnage. I would suggest on both ships adding a bit more fuel to reach the 15k tonnage cap, since more range cannot hurt and the extra speed is probably unimportant in a fleet context.
• The use of a CIC is fine, I would say probably correct. The major limitation for the extra officer modules is rarely about the ship design for ships above 10k tons, rather it is strategic - do you have enough officers to man all posts? For ships under 10k tons often anything besides an AUX is a waste and usually a weapon or sensor is a better use of space, but for larger ships the force multiplication is efficient enough to be worthwhile.
  

In the interest of keeping my shipyards flexible, I am experimenting with building two similar 15k ton ships out of the same yard. Both ships have a 45cm spinal laser, as I want to increase the overall fleet ranged damage and alpha strike. It's worth noting that I don't use box launchers at all and I only allow myself one 15kton missile ship per fleet, armed with fast, low damage size 4 ASMs to help keep the enemy's AMM spam focused on my missiles instead of my ships. My fleets usually include one or more battleships with larger active sensors (both anti-missile and anti-ship sensors) plus a handful of small active sensor scouts to increase missile hit-chance, and one dedicated sensor ship with very large passives for situational awareness. I also bring a support vehicle with MSP and fuel to keep the fleet topped off.

The Yang class is intended to be primarily offensive, with a 45cm spinal laser and 6 20cm lasers with a ROF of 10s. The idea is that the 20cm lasers create more opportunities for armor weak spots for the 45cm laser to punch right through, or hit in spots the 45cm has already gone through. I've heard that mixed high damage low ROF with low damage high ROF is optimal for causing internal damage.

The Yin class is intended to be primarily PD, but can still contribute to the offensive with the same 45cm spinal laser and one 20cm laser (because I could fit one but not an additional gauss turret).

A couple of questions for the hive mind: Is this a reasonable balance of weaponry vs armor and shielding? The shielding is equivalent to about 2 layers of armor, and there are 6 layers of actual armor. Is the speed reasonable for this tech level, or should I sacrifice some range/fuel efficiency and increase the engine boost to better control range with an equivalent tech enemy? I typically use SW BFC for each PD turret... is that overkill? My offensive lasers are usually focused on a single target, so I included two BFC (one of which is for battle redundancy) and a single ECCM. I tend to use a CIC on any ship above 10kton, is that reasonable?

Yang class Destroyer      14,974 tons       483 Crew       3,850.2 BP       TCS 299    TH 2,500    EM 3,570
8347 km/s      Armour 6-54       Shields 119-476       HTK 109      Sensors 7/0/0/0      DCR 30      PPV 74.62
Maint Life 2.05 Years     MSP 1,607    AFR 179%    IFR 2.5%    1YR 510    5YR 7,656    Max Repair 625 MSP
Captain    Control Rating 3   BRG   AUX   CIC   
Intended Deployment Time: 16 months    Morale Check Required   

Internal Fusion Drive  EP1250.00 (2)    Power 2500    Fuel Use 31.25%    Signature 1250    Explosion 12%
Fuel Capacity 500,000 Litres    Range 19.2 billion km (26 days at full power)
Epsilon S119 / R476 Shields (1)     Recharge Time 476 seconds (0.3 per second)

45cm Spinal Laser (1)    Range 384,000km     TS: 8,347 km/s     Power 53-5     RM 50,000 km    ROF 55       
20cm C5 Far Ultraviolet Laser (6)    Range 384,000km     TS: 8,347 km/s     Power 10-5     RM 50,000 km    ROF 10       
Large Quad PD Turret (2x20)    Range 30,000km     TS: 25000 km/s     Power 0-0     RM 30,000 km    ROF 5       
Beam Fire Control R100-TS20000 (SW) (2)     Max Range: 100,000 km   TS: 20,000 km/s     90 80 70 60 50 40 30 20 10 0
Beam Fire Control R384-TS10000 (70%) (2)     Max Range: 384,000 km   TS: 10,000 km/s     97 95 92 90 87 84 82 79 77 74
Tokamak Fusion Reactor R36-PB20 (1)     Total Power Output 35.7    Exp 10%

Active Search Sensor AS9-R1 (1)     GPS 21     Range 9.7m km    MCR 870.6k km    Resolution 1
Thermal Sensor TH0.5-7.0 (1)     Sensitivity 7     Detect Sig Strength 1000:  20.9m km

ECCM-1 (1)         ECM 20

Yin class Destroyer      14,997 tons       423 Crew       3,620.6 BP       TCS 300    TH 2,500    EM 3,570
8335 km/s      Armour 6-54       Shields 119-476       HTK 118      Sensors 7/0/0/0      DCR 30      PPV 80.05
Maint Life 1.97 Years     MSP 1,508    AFR 180%    IFR 2.5%    1YR 514    5YR 7,706    Max Repair 625 MSP
Captain    Control Rating 3   BRG   AUX   CIC   
Intended Deployment Time: 18 months    Morale Check Required   

Internal Fusion Drive  EP1250.00 (2)    Power 2500    Fuel Use 31.25%    Signature 1250    Explosion 12%
Fuel Capacity 500,000 Litres    Range 19.2 billion km (26 days at full power)
Epsilon S119 / R476 Shields (1)     Recharge Time 476 seconds (0.3 per second)

45cm Spinal Laser (1)    Range 384,000km     TS: 8,335 km/s     Power 53-5     RM 50,000 km    ROF 55       
20cm C5 Far Ultraviolet Laser (1)    Range 384,000km     TS: 8,335 km/s     Power 10-5     RM 50,000 km    ROF 10       
Large Quad PD Turret (5x20)    Range 30,000km     TS: 25000 km/s     Power 0-0     RM 30,000 km    ROF 5       
Beam Fire Control R96-TS20000 (SW) (70%) (5)     Max Range: 96,000 km   TS: 20,000 km/s     90 79 69 58 48 38 27 17 6 0
Beam Fire Control R384-TS10000 (70%) (1)     Max Range: 384,000 km   TS: 10,000 km/s     97 95 92 90 87 84 82 79 77 74
Tokamak Fusion Reactor R11-PB20 (1)     Total Power Output 11.1    Exp 10%

Active Search Sensor AS9-R1 (1)     GPS 21     Range 9.7m km    MCR 870.6k km    Resolution 1
Thermal Sensor TH0.5-7.0 (1)     Sensitivity 7     Detect Sig Strength 1000:  20.9m km

ECCM-1 (1)         ECM 20