I figured out Oriented Bounding Boxes. It seems that you just use the Axis-Aligned Bounding Box equations but use local coordinates of one, test, use local coordinates of the other, test again. If they BOTH detect a collision, then there is an OBB collision.
In other good news (everyone) I’ve run the first Time Travel tests. Admittedly it’s in a 2D world at the moment, but the proof of concept is almost complete which lays the groundwork for the 3D versions.