OK, I decided to try your advice and just make the two planes vertical and horizontal. It is not ideal because the planes now have to be perpendicular to each and the angles aren't quite what I want anymore, but the orbit thing works.

The cylinder thing had the same results of my first attempt, it rotates around the wrong angle.

If anyone knows of a way to have the rotation/orbit work on different angles let me know, but I am going to try it with the perpendicular angles for now.