Well guys and gals-
I finally found out what the problem was with the differential in my Mustang. I took the shims off of the 4.10 pinion gear and used my ORIGINAL shim that was on the 3.55 gears that the car came with. I put it all back together, set the backlash, and it had an absolutely perfect wear pattern on both sides of the ring gear teeth.
I drove it down my street, and there are no abnormal noises, vibrations, etc!!!
I just wanted to say thanks for everyone that responded and I certainly hope that my experience will benefit someone out there that may be trying this for the first time. Good luck and Merry Christmas to all!
Mike