ESP8266 DC Motor Won't Stop
Well, I figured out a solution, though I'm not exactly sure if it's the right one just yet.

I swapped out the Microchip TC4427 MOSFET driver in the above schematic for a ON Semiconductor MC34152. I ordered a few units of both drivers a while back, during the planning phase of this project. I swapped the TC4427 for the MC34152 thinking there would be no difference in performance, but it turns out that the MC34152 has a different internal design that somehow works better in motor applications.

The difference maybe in the varied hysteresis between the two ICs. The TC4427 offers 300mV of hyteresis between the high and low thresholds on the input, while MC34152 offers 170mV of hyteresis. Also, the MC34152's datasheet explicitly details internal 30K ohm pulldown resistor on each input and 100k ohm pulldown resistors on each output. These may prevent the "latch up" behavior I was experiencing before on the TC4427.

Either way, it works as intended now at 7.5V 2A output from the power supply. Time to see if the same can handle 7.4V 30A from a LiPo battery.