High bite carpet is a textbook example of when you need to run a diff. A 2wd car will push off the track without one!
When the diff is gritty, it's often the thrust bearing. Clean everything with motor spray right out of the package and try using Associated black grease on the thrust assembly. Put it together according to the instructions and work the diff back and forth with your hands as you tighten it...tighten a little bit, work it back and forth, and repeat.
To test the diff, put an allen wrench through each outdrive to hold them still and try to turn the diff gear. If you can turn it, you need to tighten the diff more.
Once it's in the car, hold the car up by the rear end of it and apply 1/4 throttle to get the wheels turning. Use the pit table or ground to stop one tire for five seconds, then the other, back and forth, about five times each. This will break in all the parts and allow everything to seat. When everything breaks in, the diff usually loosens up, and that's why people melt new diffs.
Lock your slipper down, hold the right rear tire and spur gear with your right hand, and try to turn the left rear tire. If you can turn it, then you need to tighten the diff. Do this until you can't turn the left rear tire. Back your slipper off the recommended adjustment in the manual, and do the test again. You should find that you'll be able to turn the left rear tire with some effort, and that the slipper shaft, nut, and spring all turn. If you can't turn the left rear tire, back the slipper off until you can.
Keep checking your diff and slipper adjustment every run or so and it will last for a long time!