Just swapping the carrier and setting backlash should do for you.
It may make a little noise if you are a little tighter than it was, but should wear in on a good run.
However, be sure to run a good name brand additive if you have a clutch type posi, and you probably should start with a few slow and gentle figure 8's and circles
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- 70 Fastback Mustang, 489 cid FE, TKO-600 5 speed, 3.70 9 inch
- 71 F100 shortbed 4x4, 397 cid FE, headers, Street Dominator, 280H, 5 lug Dana 60, 4 speed