Sounds good to me!

Sounds fun to me, I'd love to enter!

Hey, a tournament. That's a neat idea. I could run it as a forum game: everyone get X RP and Y BP to spend on a design. They enter the design, along with tactical instructions, and I run the fight. Who would be up for it?

You state self-evident facts,  imply that your incorrect conclusions from them are equally self-evident, and obfuscate by mixing in hyperbole, unubstantiated gushing and real-life analogies that don't translate to Aurora mechanics. You don't make clear what should be taken at face value, and what is colourful prose you already know to be incorrect. Stating the self-evident facts in an even simpler fashion does not help, it's the rest that is causing me problems.

If the initial salvo matters, large railguns don't deliver because they lack high single shot damage (which shock damage depends on) and penetration if that matters.
If continuous output matters, large railguns fail because they are held back badly by capacitor tech.
You want to have it both ways: "large calibre is good" and "many shots are good".
Railguns never had most advantages associated with the former, and lose the latter on anything but the first salvo if their fire rate is >10s.

You talked up the effect of the shock damage. Let's look at it.
Expected shock damage is proportional to (single shot damage)^1.3*(total damage)
A large railgun deals 2/3 the shock damage over time as 2 lasers with the same single-shot damage and triple the fire rate, but twice as much on the first salvo.
A large railgun is much worse at dealing shock damage than a laser of the same calibre. A 35cm laser has a 90% chance of dealing shock damage vs. 53% for a 35cm railgun, and expected amount is 4.7 times as large.
There is a trade-off between devastating single volleys and continuous output, but you are better off mixing weapons that are actually good at what they are doing rather than using one that fails on either account.

ROF8 Gauss Cannon x4 = Kill everything. Ok? Doesn't get simpler than that. You put a ship with two of these, next to another hostile ship, and in 30 seconds, no more hostile ship. Now imagine this: Imagine the hostile ship was hit twice by a laser, that removed some of the armor. Now you don't need 30 seconds, now you need 15. Why? Because the GC, with it's huge volume of fire, will hit internals very very often now.

I already mentioned the effect. I think very highly of 15cm lasers paired with 10cm railguns.
The raw damage output of this combination may not be the highest in a knife fight, but the format is good:
One carves respectable gashes. 4 layers deep, and many of them: it can fire every tick at reasonable tech and is quite compact at 4HS.
The other delivers more than one shot per HS, making sure that any gap in the armour will be found.
If the most practical sniping weapon (which is also good at area defence) and the finest point defence weapon for fast ships make for a good combination in a knife fight... any dedicated brawling weapon needs to be very good at it to be worth it.

Now you plug ECM into a ship, say ECM 80, and the laser has a 20 percent chance to hit. Railguns have 4 shots, at 20 percent.

Does this change anything of relevance? Sure, the railgun only has a 41% chance of missing entirely, but the important metric - expected damage - is reduced to 20% in either case.

I don't see how ECM would ruin a small laser but not a large railgun with comparable range, damage per shot, accompanied by the same fire control.

It's strange that you would claim Gauss cannons "obliterate pretty much anything"... then dismiss 10cm railguns as not very good because they are "basically RoF4 Gauss Cannons".
Never mind that their size makes them more comparable to RoF7 Gauss Cannons ton for ton,

You keep bringing up red herrings. "While my railguns are silent, other weaponry continues the job"... as it would when supporting any other kind of weapon. You have not given a reason why your other unspecified weaponry would interact more favourably with intermittently firing railguns than anything else. Hyperbole and gushing anecdotes are also no arguments.

Your last claim is unsubstantiated, and absurd it the certainty with which it is stated.
I've tried to decipher what you might actually mean, formalise the reasoning behind the claims, and make it open to analysis.
I probably should have realised earlier that this was futile.

I tried to formalise damage being frontloaded in the case of railguns, which is what your point seems to hinge on.
Using the weapons from my last post for 35cm railguns/20cm lasers, standardising for the output of a railgun salvo, there seems to be some support for it:

Turn - total Railgun damage dealt - total Laser damage dealt - Difference - Cumulative Difference - Average difference (CD/T)

T    R   L       D       CD      A
1    1   0.47   -0.53   -0.53   -0.53
2    1   0.93   -0.07   -0.60   -0.3
3    1   1.40    0.40   -0.20   -0.07
4    2   1.87   -0.13   -0.33   -0.08
5    2   2.33    0.33    0       0
6    2   2.80    0.80    0.8     0.13
7    3   3.27    0.27    1.27    0.18
D expresses who's ahead, A  "who was ahead on average so far", which we may care about as earlier damage may degrade enemy combat ability. A positive number means an advantage for lasers.
Although railguns fall behind forever after... they're ahead the turn their second salvo hits, which matches your experience.

However, this assumes all salvos are fired at decisive battle range. In practice, there will be some fire exchanged before, and  the railgun fire at turn -2 is more heavily degraded than laser fire from turns -2 to 0.
Looking at a closing rate of 20000km/s, 600k fire control range and 450/500k weapon range, this would increase all values in column D by roughly 0.25 (best case for railguns, turn 1 is the exact turn decisive range with full damage is reached) to 0.8 (worst case for railguns, decisive battle range was reached at turn -1 and lasers already got off 2 salvos at full damage and accuracy).

The following assumes the best-case scenario for railguns, which isn't much different from the safe option (the salvo 3 ticks before is only worth about 0.05, we could just hold fire).
R now denotes the number of number of railgun salvos fired at decisive range, not total damage. A is calculated for turns at decisive range.

T    R    D        CD       A
1    1   -0.28    -0.28    -0.28   
2    1    0.18    -0.10    -0.05   
3    1    0.65     0.55     0.183
4    2    0.12     0.62     0.16
5    2    0.58     1.20     0.24
6    2    1.05     2.25     0.38
7    3    0.52     2.77     0.40

Railguns performing poorly in tests is quite expected. All weapons lose DPS when they get too large for their capacitors, and large railguns don't do anything unique to compensate. Large lasers at least have penetration and shock damage that can't be mirrored by more efficient smaller weapons (maximum RoF is usually better overall, but it's not strictly better.).

What about 10cm railguns? Those have higher output than Gauss weapons per ton, unless we've researched all Gauss RoF techs (last one for 750k, eek!).
And if we do have high tech,  the largest railgun that can fire every 5s should do better in a brawl.

Actual gameplay contains many uncontrollable variables, and anything that isn't outright silly can work. I have no doubt that ships with 35cm railguns can win battles, but I can say with near-perfect confidence that they are decidedly suboptimal, without the need for field testing.
When comparing the expected value of 5d6+2 vs. 6d6, we don't do empirical research and roll a lot of dice... we can isolate and compare what's different, and know that the former will score 1.5 higher on average.

Would be nice if other weapon lines got meaningful additions, as the particle beams do in the next version.
 

Indeed, I think personally, you can basically disregard railgun tech between the 20 to 30cm range. 35 cm railguns, no matter how fast they reload, have a massive chance to do shock damage PER shot. That's pretty massive.

Quite the opposite imo. There is hope for railguns up to 30cm at high tech levels under some circumstances... but little for 35cm and above. You're hung up that some specific output is massive and enough to cause the enemy some grief. Sure, it may be... but all comparable outpus are. If there are alternative methods that do the same thing better, the fact that it's sufficient doesn't validate the weaker one.

I still think you're hung up on a metric that's not very relevant in context - power of a single salvo.
Do you expect your first salvo fired from maximum weapon range to largely decide the battle? This may be realistic with microwaves or ridiculous spinal lasers. With railguns and railgun-equivalents, this assumption implies pitting the punch of a battleship against the jaw of a gunboat.

With realistically matched offensive and defensive capabilities, we have to take RoF into account.
One strong salvo every few ticks may give you a head start in artificial tests, in practice it's mitigated by an effective range disadvantage: The ship with the strong salvo is encouraged to hold fire until it can deal meaningful damage, the fast-firing ship can open fire the instant it has a non-zero chance to hit.

35cm Railguns vs. 20cm lasers on realistic capacitor tech (10 is a good match for both):
Adjusted for space, the laser ship will fire ~42% as many shots per salvo... with damage increased to 10 and at three times the rate of fire.
If you object that capacitor-10 is an expensive tech at 125k, consider that the railgun option spent 70k more on calibre.

*

Specific examples are always problematic because one can always argue they don't apply in this or that case... but the comparison of equal-damage weapon can be broken down to simple principles:

1) For the same damage per shot, railguns and supporting crew/power typically need slightly less than 2x as much space as lasers.
2) Since railguns get 4 shots per weapon, a railgun loadout will have slightly more than twice as many shots per salvo.
3) Railguns require 3x the capacitor tech for the same rate of fire.

4) If railguns have a third of the fire rate, they have slightly more than 2/3 the output over time. Cost is comparable (same capacitor tech used).
5) If railguns have half the fire rate, they have slightly higher output over time than lasers. Cost is approaximately 50% higher (higher capacitor tech).
6) If railguns have the same fire rate, they have slightly mor than twice the output over time than the lasers. They cost approximately 3 times as much.
Lasers at the relevant sizes have exact capacitor matches, railguns not always. Resulting inefficiencies can reduce performance or increase cost.