Axles Seem To Rotate Back/forth A Lot...

I'll do the best to describe my problem. Yes, I have searched and can only seem to find issues with "in and out" axle play. I can lift the rear of my 88 mustang, grab a rear wheel and rotate it forward and backward what seems like an excessive amount. Or, grab the driveshaft and rotate it back and forth. I'm chasing a bit of a driveline vibration back there, especially when over 80 mph. Some background: New z-spec transmission, aluminum driveshaft, 5 lug swap and a friend installed a 4.10 gear for me. All within the last few months. It's on 15x10 racestars with 275's recently balanced. I'm assuming the pinion to ring isn't set properly and possibly worn spider gears, etc. Any and all help on this issue is greatly appreciated.
 
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I think the service manual has that spec in it. It list how much rotation is normal. But I'm sure that's based off of stock height tires. Been a while since I've looked at a service manual, so I could be mistaken.
 
Very small amount of play back and forth is normal, it's likely that there is a problem with the gear install, ring gear bolts loose, lash not within specs, worn spider gears. Have the guy that put the gears in pull the cover off and check his work, stuff happens.
I figure he has experience with differential setups.