SO... I am going to try and recreate the puppet with FXG files.
SO, I put all the body parts in frame one of the Flash timeline, and exported a FXG. I then imported it into Adobe Illustrator. I bypassed the issues I had before with body parts disappearing by making sure everything was broken up and (important) the vectors were colored with a color number, not a bitmap swatch (which I had done before to make it easier to universally change colors in Flash.)
I imported it into After Effects. To recap:
If you choose Composition-Retain Layer Sizes, each symbol will be the size of the stage.
|Don't do it. It'll still work, but blah.|
Quick Tip: The quick way to change the rotation point is to use the "Pan Behind (Anchor Point) tool (keyboard shortcut Y).
When you do that, you can just drag the rotation (anchor) point wherever you want!
Anyway, it was messing things up a bit, so I had to make sure all the frame rates matched and I had to redo my hand (and feet) comps to be true 29.97 fps.
I also only made one hand and one foot comp, and duplicated them on the stage, swapping them when needed.