You're right that long range shots can be worth it, but you need a 5s refire time to pull it off effectively IMO. So you can shoot it again in Final Defensive Fire.
Personally, I find lasers to make the best multirole beam weapons. Railguns have the problem of not really having enough range on the small ones. 10cm and 12cm lasers can get pretty good range while still being small enough to fit large numbers. The problem is you need a size 8-12 firecontrol.
I hadn't noticed that monster fire control! Yikes! Being able to get away with low tracking speeds is one of the big pluses of railguns... heh. Plus, 1600 BP is a lot to put in a paper thin ship and with only 2x railguns it's pd capability is limited. Tho its antishipping capability is actually pretty good if it can survive.
Let me draw a comparison with a railgun escort I made recently -
Hermes class Destroyer 4,500 tons 490 Crew 663 BP TCS 90 TH 300 EM 0
3333 km/s Armour 4-24 Shields 0-0 Sensors 1/1/0/0 Damage Control Rating 3 PPV 31.2
Maint Life 7.69 Years MSP 322 AFR 46% IFR 0.6% 1YR 10 5YR 144 Max Repair 58 MSP
Magazine 48
Atlas Thruster (5) Power 60 Fuel Use 80% Signature 60 Armour 0 Exp 5%
Fuel Capacity 90,000 Litres Range 45.0 billion km (156 days at full power)
GAU-131 (4x4) Range 30,000km TS: 4000 km/s Power 3-3 RM 3 ROF 5 1 1 1 0 0 0 0 0 0 0
GAU-333 (2x4) Range 90,000km TS: 4000 km/s Power 9-3 RM 3 ROF 15 3 3 3 2 1 1 1 1 1 0
Boresight 96/4 (1) Max Range: 192,000 km TS: 4000 km/s 95 90 84 79 74 69 64 58 53 48
GCF Series 52 (8) Total Power Output 18 Armour 0 Exp 5%
OLYMPUS Torpedo Rack (3) Missile Size 16 Hangar Reload 120 minutes MF Reload 20 hours
Goliath-15 (1) Range 15.4m km Resolution 100
HT-18 Whale (3) Speed: 25,000 km/s End: 4.7m Range: 7m km WH: 18 Size: 16 TH: 116 / 70 / 35
Small Scan System G1 (1) GPS 32 Range 2.6m km Resolution 1
ECM 10
This railgun design is low tech and only about 670 BP. A lot slower, but it actually has more anti-missile capability than the Hamburg - 24x shots at 4k tracking speed compared to 8x shots at 8k tracking speed. And its weapons actually recharge faster. I did put on the pair of 15cm railguns because I couldn't bear having only the short range of the 10cms. You could try leaving one of the 300mm railguns and fitting the rest with PD. You might even fit in some armor.
So I have the new navy designed. I assume that if the TS is lower than the target's speed, accuracy is reduced to TS/target speed. The navy will have a fuel, maintenance and collier ship with a jump engine.
Yes, it's fractional of the target speed, but it uses the lower of the fire control compared to the weapon tracking speed. (The weapon tracking speed is either the base fire control tech speed, or the ships speed, whichever is higher.) Given that you can make a 25 km/s tracking speed fire control, you must have pretty good FC tech. You probably arn't getting a lot of extra tracking speed from all the speed you've piled on the Hamburg. Incidentally, if you plan on having a collier integral with the fleet, you could probably fit some more fighters on the carrier in exchange for magazine space. Though then it cant supply as much to your missile warships.