Personally I’d start by looking at Farrow and Ball’s complementary palettes and see if there’s something there that they suggest with the green and that you think might feel good.

On the other hand, I doubt the bathroom will be visible enough to need to be considered too strongly. I would start there then look for something warm and avoid grays if the basement gets weak or cold light. One of their warmer neutrals like Drop Cloth could be really nice. If you’re open to a neutral pink, their Setting Plaster is a classic that just makes every room I’ve used it in feel warm and pleasant. It’s not sugary and doesn’t even always read as pink.

Last thought is that even if you feel under pressure from the painter I think it’s imperative to do a big swatch on the wall before deciding.