Look for series 2 or 3 XJ6 or XJ12 Jaguar 1973 to 1983.
Only the XJ12 is limited slip.
Ratios tend to be in the 2.9 to 3.1 range.
Use the whole cage as a complete unit.

Because it's a disc set up you will need to get a disc set up for the front end as well.
Here you can use the front end out of the same Jag.
Another near bolt it job.
You will end up with a beautiful riding and handling car.

I have both in my '49 Lincoln I'm building.