I spent the last hour or so tinkering away on an all-purpose 2D puppet. I've got the basic body shape, and I intend to use it mostly zoomed out so it doesn't need too much detail. The animation works fine now and I've been setting up eye expressions, basically just regular eyes and angry eyes + mouth. I put in both sets, but I had some trouble with the other set not going invisible even though I toggled it with the key frame. I ended up just moving the other pair back into the head. Of course, once I started testing it the spare set would just buzz around the head as I moved. Apparently groups can still collide with themselves, so I set each pair to not collide with anything. Now it works properly.
I will need some basic platforming logic like ladders and water, but I'm probably going to track down some good ones in the Dreamiverse rather than figuring everything out on my own. For now it's super nice just to have a tightly controlled character that still has smooth IK animation. For anyone wondering, you can set the gravity really high and set the turning rate and acceleration/deceleration to max. This gives you a character that really controls like something like Mega Man.