It going to be obvious that I don't know anything about the Greenfield drive.
This setup to looks to be a nightmare to repair but that depends to reliability the drives. Also how system does achieves anytime reverse of the drive wheels independently of each with the simply change of the pedal motion from forward to reverse. Basically how does it keeps from destroying the fiction drives when going from full forward to full reverse in a split second. Here on ZTR with hydrostatics I can literately go from full forward to spinning the drive tires in reverse in a single motion.
I think this why most manufactures have gone hydrostatic drives as they are highly reliable, reverses on the fly, and only use one drive belt to drive either a single pump and multiple pumps with wheel motors or two independent hydro static transaxles.