In my testing the inverter is the main limiting factor. The stator can saturate slightly before the inverter in repeated full-load launches from a stop, but not in general hard use, like what you would do on a track/circuit... but the stator will cool quickly while under moderate to low load. The inverter remains saturated and is hard to cool once it's reached that point because any load at all appears to keep it heated.
At one point, as an experiment, I used the Tesla cooling system with the AC compressor to pre-chill the powertrain down to 5C. This did virtually nothing to prevent the inverter from reaching max temp. With ~6-8C coolant going into the unit, it was still overheating.
I'm going to retry this sometime soon with the P90++ I think. Now that I've finally finished this project, for the most part, I'm going to do some more testing. I recently installed a second power-train cooling pump, since the dual motor cars have four pumps instead of three. I wired it to the thermal controller just like in a dual motor car so now it's happy and isn't running the three pumps at full power constantly when the car is on now. The side effect this had previously was that the car would not go into battery-loop-only mode when the one coolant valve, since it was assuming a pump was bad. Instead, when doing something like max battery power, the car was heating the pack AND drive unit. Now that the thermal system is happy I'll be able to heat the pack slightly more that I did for my dyno runs, and thus get more power.
I also plan on trying out the "Ludicrous+" easter egg at some point on this car as well. I've yet to confirm exactly what this easter egg does, unfortunately. It's possible it won't have any effect, but who knows.