As a compromise suggestion, what if the single shot weapon kept the current ROF but it was moved over to a "spinal weapon" equivalent? Which is to say, you can only mount a single weapon per hull, and maybe with a caliber bonus as well as currently happens with spinal lasers.
For a fighter or a FAC, it still works - they get a single railgun of a decent caliber and a decent fire rate. Large ships can still use them too - you can give them a big single shot spinal rail that will fire decently fast, and give it smaller 4shot railguns. But you won't get the examples of completely replacing a ship's weapons with a large number of single shot railguns to maximize DPS.
Alternately, let's look at it the other way around. People seem to be focusing on the DPS, but I think that's wrong - a single shot railgun has, at absolute best, the same DPS as a 4 shot railgun - the issue is that it's considerably smaller. Alternately, a single shot large railgun has the same DPS as a 4 shot small railgun, the difference is the single shot has longer range and (slightly) better armor penetration. And it's still smaller, which IMHO is clear evidence that single shot railguns are too good. But I would argue the problem isn't that their DPS is too high, the problem is that they're too small. Let's take a look at four weapons:
10cm Railgun V50/C3: 4*1 damage, 50kkm range, 150 tons, 26 Cost
12cm Railgun V50/C3/S2: 2*2 damage, 100kkm range, 138 tons, 26 Cost
20cm Railgun V50/C3/S1: 1*4 damage, 200kkm range, 114 tons, 26 Cost
10cm Far Ultraviolet Laser: 1*3 damage, 150kkm range, 150 tons, 26 Cost
The three railguns seem like they should be (mostly) sidegrades if you ignore the tonnage. The 10cm is the best at point defense, the 20cm has the best range and armor pen, the 12cm is midway between. Personally, I'd say I'd prefer having a single 20cm to a single 4shot 10cm, since range is king in Aurora, and that is somewhat born out by the laser doing less damage while being a nominally equivalent weapon. The problem here is the 10cm is the heaviest because of how the shot reduction is handled, and I think that's what makes the single shot railguns too powerful.
Currently railguns get a reduction of 22.5% size per reduced shot; I think this is clearly too much. If we imagine a change where each shot reduces the size by 15%, we get:
10cm Railgun V50/C3: 4*1 damage, 50kkm range, 150 tons, 26 Cost
12cm Railgun V50/C3/S2: 2*2 damage, 100kkm range, 175 tons, 26 Cost
20cm Railgun V50/C3/S1: 1*4 damage, 200kkm range, 192 tons, 26 Cost
10cm Far Ultraviolet Laser: 1*3 damage, 150kkm range, 150 tons, 26 Cost
Suddenly they feel a lot more fair. For each "step" you're paying a small premium in tonnage to keep the same DPS at a longer range, while being less viable as point defense. And the 20cm Railgun matches reasonably against the 10cm laser, doing 33% more damage for 28% more tonnage - it's still probably better, but at least the comparison is more sane. 12.5% less per shot might be better. Regardless, I think these numbers show how you can balance reduced shot railguns without making them completely useless.