You're throwing me, with door frames and crown molding in the same room that don't match. They should! If high gloss is what you've committed to for trim, I guess I'd do high gloss on the wainscoting too? It wouldn't be my top pick (semi-gloss would be) but it would bug me for it to not match the trim. I would also give the crown molding a quick coat. Eggshell on trim, even that's too high up to get fingerprints on, is not a big winner for me. Trim should at least be satin, if not glossier.
I'm not picturing the mantels - are we talking over fireplaces? 3 of them?
Well, were it my house I would do all of the things you mentioned in semi-gloss, and later go back and change what isn't, to semi-gloss to match. But if high gloss is working for you, I'd just do it all in high gloss. Either would be ok against the brick I think. That bathroom will look so much better!
In your case, I'd do all high gloss (and repaint the crown when you can). If you were repainting everything I'd do semi-gloss, but that would be a lot of work to change now.
ditto everyone that semi-gloss would be my go-to but high gloss fine since that's what you've started with. In a convo with my paint guy recently he was saying that his gloss is really like a semi-gloss (semi more like stain, etc) so maybe what you have isn't really all that high gloss. I mean does it look really shiny like it's wet all the time? That kind of lacquer finish is what I think of as high gloss.