The new motor I received from Makerbot Industries worked well, but a couple weeks ago it began stopping mid-print just like my old motor did. However, I found a fix!
The trick is to use a relay board to control the extruder motor. There are two downsides to this, though: 1. you use up a port on the relay that could have been used by the HBP, and 2. you loose all speed control of the motor. The loss of speed control wasn't too much of an issue because the DC motor was only off or on, and the loss of the HBP was alleviated by covering the build platform in blue painter's tape. Blue painter's tape, in fact, proved to work better than the kapton tape surface (I'm now able to print raftless!).
Overall, I'm quite happy with the result.