Okay, so since I started this a couple months ago I haven't given this another go, so I thought I'd take another crack. This one looks really good, I think. It's not quite as saturated as I would like, but if you go any further you get all sorts of artifacts and weird things happening, but the sort of "essence" I was talking about comes through.
These were the settings I used in VLC:
Lessening the bad skintones wasn't quite as difficult as I thought, compared to last time I basically just went more towards cyan in the hue and held back on the saturation. I gave the contrast a decent kick as well, which looks nice IMO (I think I could have gone further though), and brightened the image a bit.
I used a sharpening filter as well, which I think looks really nice, but you can't tell in the caps. Anyway, this is what I ended up with.
You can still see a bit of popping in the reds, but it's pretty tolerable IMO. If there was a way of desaturating the reds only just by a bit, which would give skintones a further help, I would say this is a pretty decent "theatrical look", even if it lacks a little bit of the vividness I would like.