Im an experienced 3D guy and After Effects user, and this is how I'd achieve what you're after...

If I were doing one object going behind / in front of another, Id just be doing the 'split layer' thing each time they needed to swap.

Effectively, you find a point in your timeline where the objects are not overlapping visually, then select one of the layers (you said the cubes were rendered on seperate passes) and go Edit > Split Layer from the menus.

This will break your layer into two layers. Then, just organise your layer order so that one is behind the other at one point, then behind afterward.
You will need to be careful though - any effects you apply to the split layer will have to be replicated onto the other half of the split layer. Generally, split your layers as a final step, when all fx / transforms are done.

No mucking about with z-depth, just straight RGBA sequences.

Let me know if any of this is unclear and I'll elaborate.

Dan