About the cheapest conversion for a rear a lot stronger than an 83 /4 is ( or was) a truck dana with a clutch type posi and a ratio you can use. I found a Dana 60 with 4.10 gears. A used set of 35 spline axles , a disc brake kit, spring pads and I had a strong rear for my 535 stroker on the cheap. The posi didn't survive long but some home made shims added to the clutch pack in the diff locked it up. As I recall it only took one shim made from the end of a 3 lb coffee can to do the trick.
This was done 40 years ago so I have no clue as to what dana 60s go for at the boneyard or what posi's, or ratios are available now days.