[JesseK]

I would say that it would be an addition of traction on carpet if the corners had paired mecanums. The pairs would be aligned with a slight offset in order to fill each others' gaps more effectively, much like the way one offsets a pair of omni wheels that are bolted together. I believe a pair of mecanums is still wide enough to allow you to mount the CIMs the same way as well, so you'd still have the same space-saving design as seen above.

Three mecanums side by side is a power loss unless the surface has small bumps that are very close together (like diamond plate). In a bumpy case, it's difficult to predict angle and surface area of contact, so more is probably better to assure the bot gets full traction.

This is still a fun design to ponder, even if some of its iterations are impractical on the FRC field.