Wow. That was an extremely impressive and helpful example you posted. Yep, that pretty much summarizes absolutely everything I needed. Thank you!

Interesting, thank you. Sure enough, removing the mass piece did fix the first problem (instant crashing). As for splitting it into two objects, though, how would I achieve that? Would I have to create object.box.shape1 and object.box.shape2? And if so, how do those retain a proper angle and behavior?

So I've been using pixel-perfect collision using a bitmask with my game (I've only been checking the overlap of a previous box-collision, and I only check every 1/16 pixels (4x4)), which has worked perfectly for images that don't change angles. However, that is proving quite difficult with a bitmask...