Hi Ross,
I haven't used this particular motor driver, but I rather doubt that the BRAKE pin is designed to stop a motor quickly. Especially if there is significant inertia involved. When you pull BRAKE low, the high-side FETs will short-circuit the motor windings, which can result in a tremendous current, depending on motor, inertia, wiring etc. The overcurrent protection won't help you, because the EMF current doesn't flow through the sense resistors when you do this. And the FETs may be dead long before the thermal sensor discovers that something is wrong. So, yes, I would definitely guess that Back EMF killed your chip.
The BRAKE feature is probably designed to (more or less) hold the motor in place, once it is no longer rotating. If you short the wires on a DC motor, and try to rotate it, you can probably feel what I am talking about.
I can think of only one relatively simple thing to try: Gradually reduce the speed by reducing the voltage on VREF when you need to stop.
As this device only has slow decay mode, I don't think it will increase the supply voltage while braking. Otherwise, there are simple methods of dumping the excess power in a resistor.
A more clunky hard-core method could be to use an old-fashioned relay to connect three power resistors to the motor windings when EN is low.
