Wheels spinning when turn.

Lock in that power divider and you will be buying a new one. You have two very different circumfrence tires on each axle, so each wheel is spinning at a different speed. You lock in and now both axles are trying to turn the same speed. You will bind up the gears and break something big time.

 

We really don't know if there is any difference in diameter/circumference.
All the OP provided was tread depth for front & rears. Tread depth differences may not apply here. Reason below...
Possible he has different tire manufacture, different tread style, between the front and rears, yet has identical tire diameters.
The diameter is all that counts. I think we can agree on that.

Now both front and rears should also have a "tolerance", as far as what is the max size difference you can run on a locked power divider.
Rarely will front and rear drives be "exactly" the same, down to the 1/32", just because of different wear when the truck is driven countless miles in a disengaged power divider mode.
My only question, and I don't know this yet (but digging to know), is what is the maximum tolerance that is "safe" to run with a locked power divider, as far as small difference in front-rear tire diameters. Certainly "any" difference is not good, but there must be some acceptable tolerance.

Offhand, I'd guess (keyword is guess) it to be about 1/8" to 1/4"(max) difference in tire diameter, max.
But any guess is not acceptable to me, so I'm curious to dig up exact tolerance.

 

Locking the power divider in for long period of time is not suggested that I knw of , Most trucks that I have driven and worked on Usually had a alarm to alert the driver if he power divider was locked in . I wasn't a true Diesel mechanic , but a fleet mechanic for 5 years seen many a rear end and or a universal broke , finding Jewelry in the rear diff , was exciting ..