I got it solved while still using Cinema4D! The solution wasn't exactly what you suggested, but I suddenly got an idea related to this and that worked! Basically I created an expression for X, Y, and Z for each object out of position based on the amount of rotation I'm doing. I used Mathway which has a feature where you can plug in a bunch of X Y values and it will generate an equation that satisfies the values.

Here's another video demonstrating what I did if you're curious: