I did some experiments hooking up the motor controller to a bench power supply. Here's the motors running on full speed with a 5V, 1A current limit (they're running at about 422mA).
I experimented with current limiting: a limit of about 398mA causes the voltage to fluctuate between about 4.7 and 4.8V.
Since the Jetson isn't connected to this, the power supply doesn't cut out - which means the motors just get a lower voltage, and they're okay with that.
I had a "genius" idea; I could connect the motor power supply to the 3.3V rail instead of the 5V rail to act as a current limiter. It sort of works, as long as it's not on carpet... there's just too much friction, I guess. It'll at least buy me some time while I figure out a better power solution.