I had the same problems. I had upgraded the stock motor to a 37 turn motor, whic is a lot more powerful and this may have led to some of my....er...pains.
I ended up curing it, but it took some time, money & work. Here is what I did:
1) I replaced the driveshafts with the ones below. You will notice they have a pin that goes all the way through the driveshaft, pin, and provides a secure connection. This, however, led to a problem... my pinion gears and output shafts on the transmission were not drilled.
Xtra Speed Steel Center Universal Driveshaft Axial SCX10 EP 1 10 RC Car Crawler | eBay
2) I bought a set of cobalt drill bits, and - using a drill press - drilled holes in each of the pinion gears to allow the pins from the driveshaft tgo through. Yes, I had to take the differentials apart, pull the pinion gear, drill it, and reassemble the differentials.
3) About this time my transmission died. Instead of replacing it with the same plastic-geared one, I upgraded to this, all metal geared one. The output shafts on it came pre-drilled, so that was fortunate.
https://smile.amazon.com/gp/product/B01A1GT7ME/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1
I did use locktite when I reassembled the driveshafts, and they have not come loose in a lot of bashing (even by my 6-yr-old who loves to alternate between full reverse and full foward). :roll:
A long, frustrating road, but it will completely "cure" the problem, as well as beefing up your Everest a LOT!
Hope this helps.
Terry