But anyway, I fear this discussion is fruitless. You appear perfectly willing to ignore any and all flaws in your design.
"days" is not a gun battle, that is a protracted strategic skirmish, and there will be extensive losses in that time, and railguns have faster projectiles with flatter trajectories and less distance correction. There is a difference between ignoring flaws and assuming that something cannot be practical in a highly speculative game just because it wasn't explored in history. Would it be difficult? Yes! Would it work? Deathball? What of submarines? In practice, submarines are massively lethal against merchant shipping. If we built a submarine it would likely drop their benefits from naval advantage by two levels regardless of what they did about it short of some sort of catastrophic intelligence failure, but have almost no effect on determining naval advantage. But within the game's context it is all fleet battles, so all your submarines are clustered around your fleets, trying to weave between escorts to dump torpedoes into battleships in the midst of a battle.
Railguns are actually very similar to explosive reactive armour. Both use what is, basically, existing elements. Both have performance requirements which are rather difficult to get right. The E.R.A. has the difficulty of detonating without damaging what it is protecting, without chain-reacting, and without detonating on impacts that are far too weak to pose any threat.That ekes your performance specifications up to the level that it starts requiring some development. railguns need some development of power systems and equipment wear, but produce clearly superior muzzle-velocity. And if we can come up with a solution, even a not-particularly-realistic one, such as having rails be a conductive paint over a resin backing and thus can just be painted back on after they wear off, then there is a decent chance that it will actually work...
I am not advocating railguns out of some antagonistic glee over throwing science fiction into a W.W.II game, I am just trying to find something somewhat interesting, rather than proposals that are little more than links to or paraphrasings of wikipaedia articles. I mean, if we are going to crib historic designs, let's do it honestly. How about we spend a design purchasing a single Yamato-class and have it as a fixed national effort?