Since I haven't got any LiPo-packs lying around, I'll have to start with the ESC-programming.
You're mentioning the the punch/start setting...the default setting is "level 5", I don't really know what this option does to the car. Is there a correct setting or do I have to figure it out/tune it myself?
There's also the initial start force setting...nine different options here as well. Could it have anything to do with that?
Ok, yeah, start with the programing and let's work from there.
I should clarify, there's not really a "correct" setting for the punch/start, it comes down to your car and driving style. First off, to clarify, the punch/start setting is essentially how hard your car can accelerate from a standstill. Your punch/start settings control how hard your car can do this. IIRC the higher the number your punch is set at, the harder your car can accelerate, which means you'll be able to do wheelies more easily, more "power slides", get up to top speed a tiny bit faster, ect. and vice versa with a lower punch/start setting. Now, there's more to this, there's a reason why everyone doesn't just set the punch/start on the highest setting. The higher the number, the more strain/wear/load you will put on your whole drivetrain (from the pinion/spur, to your driveshaft, diffs, CVDs/dogbones, and your wheel hexes, and so on), including your motor, ESC, and possibly your battery (which could be indirectly affected, but probably not by a massive amount).
In other words, higher punch/start equals more drivetrain wear and possible breakage, versus setting the punch on a lower setting. If you're heavy on the throttle and are accelerating all the time, you'll probably not want the punch too high. If you like tricks and stuff, you'll like a higher punch. Dislike maintaining/replacing drive train parts? A lower setting will do you well. And obviously, if your car is older/not built like a tank, you'll probably want to shy away from high punch. Hope this helps, try adjusting the punch/start! Also, are you getting the same issues with the ESC when going forward only?