Any non electric 4 speed autos for a 360 mag out there?

I am rather sure that both tires will have power because I have left two-wheel burnouts going straight, and only one tire spins around a turn. Hmm. It is an 8-3/4, but I wonder why it is doing this if it isn't the norm. Would the traction bars make it do that, well ladder bars?

When in a turn, the power has do divide between the inner wheel and the outer. If it didn't, you wouldn't be able to turn at all unless one of them spins. Around a turn, depending on the speed, some of the weight on the rear of the car transfers to the outer wheel. This makes it easier for the inside wheel to spin.
If your diff is a cone-type SG, then it may be set up a little on the tight side. The clutchpack may not be slipping, which is the whole point of having a Limited-Slip-Differential. It is kindof acting like a spool.
To rebuild those, I have made a stub axle that I clamp in a vice. Then I drop the diff-case on that. Then I have a second stub with a big ol' nut welded on the end,that I drop into the top side-gear. Then I can put a torque wrench on it and measure the breakaway torque, and the turning torque. Of course the clutches have to be lubricated prior,with the same LSD-oil that is gonna be in the car.
Using this method I can tailor the diff to the application.
In my car with no traction aider, and with 295/50-15s,and a cone-type LSD; I have found by repeated testing and adjustments, that for turning torque ;
100 is not nearly enough. And
110 was good with 245/60-14s, and a 318.
120ftlbs is a good number for my HO 367, and 295s. And at
140 it acts like a spool. Until install the 325/50-15 BFG Comp T/A Dragradials. But it's still a little tight, slipping the inside rear tire on less than perfect surfaces.

So I target 115 to 125. Adjustment is by shimming the side-gears, and the oil concoction. For me, 120 has been just right.

You could test yours on the car, but to be accurate you would have to make a tool to mount onto the axle flange, so you could use the torque wrench.
If you just want to make sure it ain't worn out, that's easy. Just jack up one side of the car, and chock the opposite side wheels. Then put it in neutral. And attempt to rotate the jacked up tire.
Can't do it, is too tight
Spins easy, is worn out
In-between, is a judgement call, based on amount of effort required and degree of misbehavior encountered during usage.
If you drive the car off the jack during testing, you forgot to chock the opposite side tires! Don't do that.
EDIT for clarity;
that is to say; if whilst attempting to turn the tire with your arms, you accidentally push the car off the jack you will get seriously hurt. So make sure the car cannot move forward or backwards; chock the wheels on the opposite side.
You could start the engine and put in in gear,rev it up a little and see if the jacked up tire spins. If it doesn't and you put more power into it, you could drive it off the jack and damage the car. But you would have no idea of what the actual turning torque might be...... so don't do that.