... So I would expect something in the diff. It sound like you need to pull the rear cover and look inside there. You need to drain the hydraulic oil to do that. I do not see anything external or simple that would allow the front wheels to drive and the rears to slip.
I would be cautious on how you use the tractor. You are putting all the torque to the front drive system, which it is probably not designed for. You have the chance to cause a lot more damage driving it.
My thinking centered on a rear diff failure but my ignorance of how the eHydro works confused me ... your comments have been a great help and it's making sense.
Sound advice on the machine out of service, as well. It's heading to the tractor shop on Monday ... too much of this is beyond my shade tree capacity. Seems like the kind of problem that requires the attention of someone who knows what looks right and what looks wrong, in this case that someone isn't me.