You're gonna love this. Water + paper towel.
Basically I wet the area slightly, wait a couple seconds, and wipe it off. So I'll wet one area, go work on another area, then come back and wipe the first area off. I'm being very meticulous and making sure not to even touch the good paint with the paper towel (even though the paint is hard now), so I make small movements to avoid overwiping. I've had to use my knife to score a couple places with particularly thick paint. Part of what I did wrong previously was that I wasn't using a fresh blade in my xacto knife. Most things I use it for don't require razor sharpness. This does.
So I take a dry piece of paper towel and knock the loose flecks off, and the particularly hard to reach parts (around the hinges and between the 2 doors' frames) I'll take the point of the knife and lightly pick them off. I'm 3/4 of the way done (took a break so I don't make a mistake rushing) and figured I'd share the absurdity.

I still have a couple places where I may need to use the card + wool technique though. If you look at my pic and see the far lower T molding, you'll see where I got red paint all over the inside edge of the side, which is still meant to be black.