The problem going in a straight line:
you say it happens under heavy acceleration? Does it NOT happen when the car is moving, but you're not accelerating (just coasting)?
If so, it's your differentials causing the problems. Make sure they are clean, a little piece of sand in your differential can make a world of difference.
Also, on the bottom of the chassis, near the back, there is a slit where you can see through to the spur gear... I put a small piece of duct tape over that to keep sand out of the gears, and it has helped a LOT!
At this point, I've trashed my rear differential, so I actually locked it with super glue, and it's great for drifting, and takes off faster, and in a much straighter line now. BUT... you can't turn as fast UNLESS you are drifting.
I'm going to be trying various differential combos; RC18T, MIP, all that jazz, and keep swapping stuff until I find the best setup.
Since I use my car for drifting some days, but for racing other days, I will most likely be swapping differentials a lot...