You definately have the diffs too loose. If you listen closely you'll hear a screeching noise too. That's your diff balls going bye-bye
When re-building a diff here's the procedure I follow:
1. Assemble the diff per the instructions
2. When tightening the diff, tighten till the balls and diff rings just come into contact. At this point the diff gear can be spun easily while holding the outdrives.
3. Tighten the diff slightly maybe 1/8 of a turn. Hold the outdrives and spin the gear. It should be a little tougher to spin now.
4. Repeat step 3 till it's difficult to spin the gear while holding the outdrives but the diff action (spinning one outdrive while holding the gear) is smooth.
This should get you close. After running a pack through the car, check the diff action and slippage. It may need to be tightened a bit.