I've got the same tractor, same problem. I put mine up on jack stands and repeatedly tried (un)engaging the front drive, each time looking to see if the shaft moved at all, and it did not. So mine is not driving out of the transmission. I first thought it felt like the shaft/yoke was not working. But fiddling with it I could definitely feel the gears when carefully working it while running. But in/out, at no time was there any odd noises. So now I'm thinking broken shaft or gear, or maybe get lucky and find a sheared key.
Do you have a FEL? When I got mine, the directional AG tires were on backwards. All combined it leads me to consider that it might have broken the drive when trying to back out of a "bad place" with 4x4 and a bucket load. That would put almost all the drive forces on the front drive, which it's not built to handle. My main hope is that it was engineered with a "weak link" to protect the more important (expensive) pieces from catastrophic failure in such cases. I've not found anything to back that up, but still hopeful.
I keep trying to take time to go into the top side for a look around, but other things have prevented me so far. May be a good time when I do the pending fluid change. But for me, unlike you it seems, the front drive is just nice to have, not necessary. As such, I'm not that pressured to fix it, and it keeps getting pushed back.
Good luck and be sure to post up when/if you resolve this.