LOL -- You're pretty quick landyacht318 !!! That was exactly it.
In other words, I think he was telling me he didn't want to do it.
And that was just to replace my rear end with a JY rear end -- no new parts at all.

Anyway, I'll deal with this when I get back.
The more I look at it, the more I think I can rebuild it myself.

Thanks

 

Late update:
Since this old thing has over 200,000 miles and I bought it used, I had no idea when the diff fluid was changed. Even though it was ok as far as the fluid level was concerned, I had the diff flushed and new fluid put in.
Viola, all of the high pitched whining and ringing is now gone. I still whines, but nothing like is used to. I've had 2 other Dodge vehicles (new 1975 Sportsman 200 van, and a new 76 Plymouth Fury) and they all have had diff noise. Since there is nothing grinding or scraping, I think I'm just going to drive it as is for a while.
Flushing and refilling the diff with fresh fluid eliminated about 80% of the noise.
Thanks to everyone for your help.