Did you remove the driveshaft when checking the joints?Ok, so u-joints appear and feel ok. Tight but not overly so. Nice and smooth movement.
If the pinion is loose, the gears have been meshing improperly.Pinion.....well let's just say it ain't good. It does have play but the play seems limited to in-out vs up and down or side to side. I couldn't locate my socket that fits the pinion nut during lunch today.
Moderate chance you'll NEVER get those gears quiet again because the wear pattern has been disrupted.
OTOH, it doesn't really hurt to try.
Not having high hopes is a good idea.1. Check and see if the pinion nut is loose. If loose, attempt to tighten it properly. Refill and see if the issue is resolved. (Not having high hopes)