A squirmy feel might be from the diff 'ear' bushing - it's not solid rubber like the six-cylinder cars and tends to fall apart. Sub frame bushings are also a common failure on high-mileage cars.
It took me about two hours to drop the rear diff, about the same to get the replacement diff in. Happily I only stripped one bolt (on the diff speed sensor, I spliced the harness instead of swapping the sensor). I did PB Blast every bolt I could get at a day ahead of time.
It's really a marvelous PITA (especially on the left side) unless you take the rear exhaust pipe out. Having a helper would be great too - you can have them lock the brakes while you're unbolting the 12 half-shaft hex bolts and the four drive shaft bolts. That way you can spin the wheels to access all the bolts at once. I stayed under the car and used a big honkin' screwdriver wedged between bolts to keep the wheels from turning.
If I had to do it again, I'd seriously consider dropping the rear exhaust & the whole axle & fix everything while I'm in there. To drop the axle you have to unbolt the seven sub frame bolts, the ABS sensors, the calipers and the parking brake cables. Not all that hard - and it makes those 17mm bolts on top of the diff really easy to get at.
Don't forget to check the parking brake while you're in there, when you're replacing the pads it's a perfect time for that.
New swing arm/subframe/diff/sway bar bushings, inspecting the CV boots, new brake lines, new fuel lines. I'd estimate it's about $500 in parts alone, but once replaced it'll last another 20 years & I can check it off the list. I'm going to get a donor subframe to rebuild & repaint, then replace all the rubber and the shocks/springs at the same time. You'll want a late model six-cylinder for the larger rear bearings like our M42s have. Early e30's have narrower bearings, as does the 318ti and Z3 four-cyl.