We replace the lame old open rear differential with a used Auburn style posi unit out of a 1987 Chevy truck that also had a 12 bolt rear end. The gears are swapped as well, same ratio, but we went with the ones that came with the posi unit. We replace the carrier bearings and pinion bearings in the process. We finish up by setting the backlash by feel. I failed to discuss this, but as you may have noticed, I check backlash all the way around the ring gear to check for potential runout. If you do have runout, you'll never get an accurate backlash reading unless in the same exact part of the gear and will have the problem of the runout itself.
Bonus Information: Look forward to seeing a new engine going into the Big 10 soon!