My first though it they would deny it out of hand as it uses a motor, which as you posted when attached to a trigger device they concider a machinegun.
Can a stepper motor be wired so that it runs while ignoring it's controller signal? If so, it's no different than a normal motor and they would deny the application. That "rapid fire" feature you mentioned would definately get it denied, or if it was possible to modify the controller circuit to accomplish that they would turn it down. The "stored trigger pulls" mode is iffy, but I'd tend to think they would rule against it.