So I just got my 1970 Coronet done and on the road. 440 4 speed, great car. Rebuit 440, rebuilt 18 spline 4 speed, shifts like butter.. Heck why worry about the Dana, how can you hurt one of those??? So now I 've got a nicely done car with a Dana that howls like a bit%$# when you let off the throttle. Under acceleration/cruise it is is pretty quiet. Take your foot off the throttle and oh boy, can you hear it whine. It's the original rear (4:10) so I doubt the backlash suddenly went away, so I'm thinking it is one of the bearings. Questions is:
If I buy a bearing kit how hard is it too replace the bearings? I know I can pull the axles and press new bearings on those. I think I could remove the carrier and replace the bearings on the sides of that (keeping the original shims all together, but seems to me to be almost impossible to replace the pinion bearings without the training or tools to adequately do that job. Am I wrong??
I hate the thought of taking the whole assy. out of the car, and taking it to a shop.
any suggestions??

Make sure the pinion nut is tight. If loose it sucks back into the case (when let off the gas) and changes pattern. I would replace all the bearings if you have to take apart. I also wouldn't chance the setup, redo it with the proper gauges-tools. Better in the long run.

Classic symptom of a loose pinion nut.

Lots of shops will overhaul the rear in the car.

In theory, you should not have to change any settings, shims, etc. if the unit wasnt toyed with since oem assembly.Done many late model pickups, and never had a problem. However, this units 40 years old....maybe other hands have been there.

It's possible other hands have been there I have no way to know. I did take the cover off before I put it back under the car and it was very clean and the ring was date coded correctly. I made the ASSUMPTION that it would be fine. I have thought about checking the pinion nut for proper tightness. As I've gotten older, I don't have the same arm strength as I had 20 years ago so it kind of intimidates me to try that, but I guess I don't have anything to lose.

sounds like a loose pinion. I think it is supposed to be torqued to 250 ft/lbs

If the nut is loose enough to cause the issue, it will be pretty obvious. And while it needs to be Loc-tited, torqued and staked just tightening it up as much as possible will prevent further damage. Then find a local shop with a lift and a big Torque wrench

I've always used a Makita electric impact to tighten mine, no lock tight. Race cars, street cars, not one has came loose. That thing will tighten Superman's nutts.

Also a classic symptom of a worn ring & pinion.