It's been a fruitless search in the DFW area for a 8-1/4 or 8-3/4 for my '64 Valiant, so I'm going to have to fix the 7-1/4" or risk a breakdown this summer. I don't drive it hard, so it's probably enough differential for my demands at this time.

The noise is a low, steady growl that does not change with load or when turning. The noise increases somewhat as speed increases, so I'm guessing it's a bearing, but I don't know enough about the unit to make an educated guess.

Any experts have an idea of the exact cause, and/or degree of difficulty to repair? Any idea what an independent garage charges for an overhaul?

Most likely axle bearings, an easy fix.
Call around for some quotes, this is one of those jobs that has a wide price range.
Last time I bought the bearings they were around $30.00 each, then another $40 to press them onto the shafts. (both)

If you take it to a shop to do the whole job, they will hit you for a couple of hours of R&R labor. With air tools and axles ready to go, I can do this swap in about 30 minutes.
DD

Thanks for the info, Doc. The only thing that made me not suspect axle bearings was the fact that when you turn a corner, there is no change in the tone. Bad axle bearings on a 8-3/4"'s that I owned have always been easy to diagnose by loading them in turns and listen for a change in the sound.

When I was selling Mopars at a dealership in '64, we often had new cars come off the transporters with bad axle bearings. The factory told us that it had to do with the way the cars were chained down during shipping. If the cars rocked fore and aft under pressure for a few days, they would wear the bearings more than driving thousands of miles would do. It was probably our most common warranty repair.