Also if you can get someone who has a lot of experience with motor control they can get you going pretty quickly. I'm assuming what's in the Tesla is a brush-less DC motor and there are a few things you can do (especially since you're on some serious batteries in the Tesla) to push some serious torque at the startup curve. You're probably only running a modulated power start for a few seconds. After the first few seconds you're shoving the full amperage into the motor.
You are right about the startup torque. AC induction machines can produce full breakdown torque at zero speed, but this does require high current (but luckily not high power because the applied voltage is still low due to low motor speed).
Another limit is the junction temperature of the power semiconductors in the inverter(s). I think Tesla uses liquid cooled inverters, but this typically means there isn't much mass to act as a heatsink (relying on the liquid coolant instead), so overload times are typically very short. I'd would guess this is actually the limit in their design. In other words they can put very high currents into the motor for a long period of time before it thermally overheats, but way before that time they have to reduce the current in order to protect the power semiconductors in the inverter.
For a much better explanation than I can provide, see https://en.wikipedia.org/wiki/Power_band#Electric_Motors
