Guitar Nerds Anonymous

Not sure what to do about the action. I've never taken a neck off but am up for trying.

If the neck is bolt-on then it should be easy enough. Find some of those wedge-shaped shims (stewmac?) to fix that action. I guess you'll need to buy the blank ones and drill your own holes in them since your guitar probably doesn't have one of the common patterns/spacings. No big deal though.

But the bridge also seems like a few mm could be taken off the bottom of the top part.

I'd be more careful with that, changing the break angle can really mess tuning stability up.