Ring and Pinion - What Brand ?

get a ring and pinion set made by US GEAR ( NOT US Standard Gear ) -- made in the USA ,,, available from Summit , Strange Engineering , Quick Performance etc . --- Motive Gear bought out Richmond Gear several years ago , box is Richmond but a Motive gear inside--
your problem is a set up issue -- pinion depth shim incorrect or more than likely pinion bearing preload not set properly
if you buy a set of US Gears , they come from the factory with a gear pattern run on them --take a picture of the pattern as this is the gear pattern you should strive for in your set up then get the pinion bearing preload right ( 20-25 inch pounds new bearings -- 10-15 used bearings )
If you want the run-in gears from U.S. Gear note that they are at least 1.5X the price of the regular ones. They sell the 8" Ford "everyday" gears for $220-$250, but the 8" Ford run-in "Lightning series" are $350-$370. I have never heard anything bad about them, however.