I installed one in an open rear so I cannot help. However, I'd call Summit's tech line (not the 800#) and ask them. It is a strong unit that is 100% posi in straight lines.
I have it in now and there is no way this is right. It is looser then a 50 cent hooker. You can turn the wheel and it spins nothing. The gap in the middle is huge, the big pin that goes through the middle prevents the locker from meeting in the center and the little springs and pins along the inside of the locker are almost about to fall out. This is sad somebody help!
You NEED an open carrier for a lock-rite. I think it says that in the instructions. Mine did but it was a Chevy. Read the instructions again.
Anyway, the clutches space the side gears out so obviously a posi carrier won't work. Think about it... where is the washer the side gear is supposed to ride on? There isn't one because a traclok has clutches instead of a single washer.
Go get a used OPEN carrier and bolt your ring gear to it. You may need new side bearings. Hopefully the carrier shims will be right. The carrier should go in very tight. You don't want more than .014" of play and at least .005". Don't quote me those #'s are off the top of my head.
I had a lockrite in my Chevy truck 'til the pinion and carrier shattered. Now it sits on a shelf in undamaged condition. They are very tough. Other parts will break before the lockrite does. It should be illegal to sell these for c-clip axles!
Use the thickest gear oil you can find like 85/140w and top it off with a bottle or two of Lucas. That helps quiet the clik,clik,clickety noise around corners while coasting. Do not goose the throttle while cornering or it becomes a spool all of the sudden and understeers bad. Lockers take some getting used to.
Of course if this isn't a lockrite and one of those new powertrax things it may be smoother and not click so bad