UPDATE: I am now able to get the drive to Fast Forward reliably. The Fast Forward leaf switch wasn't making reliable contact, bent it a little and now it works 100% of the time.
I am still not able to get my drive to Play, however. Does the drive require a signal over SIO to start playing? If so could this mean a bad connection to the relevant pin on the Atari 600XL or broken SIO cable?
From what I can tell by looking at the drive, the Drive actuates a common leaf switch for Play, Fast Forward and Rewind. For Fast Forward and Rewind, this switch is ANDed to determine motor direction. I'm guessing for Play, this switch is ANDed with the command from the computer.