Some controllers are overrated, but any 1500W controller should stand up just fine to the task of driving an undamaged 350 watt motor.
I would recommend that you do an ohm meter test on your motor. If you do not already have one, go to the hardware store and buy a digital multimeter. I suspect that your motor is bad and is blowing controllers.
If you do not feel like getting an ohmmeter, I suggest that you open up the motor and take a look inside. If the windings are black, charred, or barbecued, your motor is toast and you need a new one.
When in doubt, get bigger MOSFETs!