The suggestions above are ingenious. However, we've moved away from BLDCs to synchronous motors, which you might use a BLDC for in this scenario.
My comment on sine-wave drive and the need for sensors come from the fact, that with sine-wave drive you have no meaningful back EMF and can not use it for commutation. Sensorless BLDC drive only works with trapezoidal drive, which again leads to torque ripple that is unwanted in your application.
The working mode for the sensorless controllers that I know is as follows:
1: DC exitation. This means, that the motor is brought to a know state by applying DC to the coils and thus rotating the rotor to a known place.
2: acceleration. A 3-phase (others are possible) frequency ramping drive voltage is applied to the motor, accelerating it.
3: At a certain point, the back EMF is large enough to be used for commutation. The motor is now in normal running mode.
Now, in this application, you could replace (3) with just forgetting the commutation and regard the motor as a synchronous one. It might work. However, just applying the frequency ramp and not bring the motor in a known state first is questionable, so a bit of extra logic is required for the circuit.
ncbuska: if we are looking at a BLDC as a synchronous motor in this case, why do a PLL? As I said, the back EMF would be meaningless, and the generated frequency for the motor would suffice. The feedback from the motor would just be the generated drive signals, and they are known already from the drive circuit.
Benta.