so every game stayed in the same no castling variant
and you're right, this rating is for that constrained variant, not full chess.
For castling you should be able to fix this by specifying that castling rights have been lost in the positions you give it.
For the others I think you would need to filter not just when giving it the list of allowed first moves. You'd also have to make it not consider en passant and promotion in the search, by modifying its move generation.
The static evaluation would still be off a bit, but that probably would not have much effect most of the time.
From what I've read it is feasible to train a new neural net on a decent home computer in maybe around a week, but that's probably overkill for your use of figuring out how strong your engine is at no castling/no promotion/no en passant chess.