I think I figured it out… Since I have these paths on both layers operating as masks, it somehow gets in the way of copying/pasting… I tested this on a really basic comp. Without any masking, it works fine, but with masking (and a few edits to the path) the only thing pasting is the first version of the shape I made… Also selecting the Path sublayer of the Contents just gives me a path with no fill, stroke or effects…
Also, pasting the shape reverts to the basic shape with no transformations. I’d resized it in the first layer, and the pasted version went back to 100% no matter how often I copied… Weird.