Have you considered buying tires with some tread on them? It's highly unlikely that every big rig that's ever been produced in the past 75 years or more would have been able to haul untold millions of tons of cargo if all of them really needed a locker to get the job done!
Jerry
I have brand new 10R22.5 retreads! Nice tires. The other day I was in wet grass and had to back up a hill with a full water tank on the back. Right tire spun out and there I sat. Most of my trouble is on ice in the winter though, and it always spins one side immediately and then all momentum comes to a stop. An icy slope is also where I had a problem with the parking brake not holding it, since it's an open diff. Creates a dangerous situation. Again, this is all with very nice tires on it. I can send pics if you'd like to see them.
I live in the mountains, lot of steep terrain and snow/ice/mud.
I should also mention I swapped the engine with a new BBC with 525ft-lbs of torque, that doesn't help, haha.