Single phase motors often poorly at lower frequencies but in this application where no torque is required you're probably fine.
Here's some drives which are designed for single phase motors.
http://www.anaconsystems.com/text/opti_e2.htmlBut they're not cheap. You could try is looking for a cheap VFD which can be operated off load so you can connect the motor across two phases, leaving the third unused.
Regarding the circuit you linked to.
It should to perform PWM to reduce the voltage at lower frequencies otherwise the motor could overheat; a commercial VFD will do this and you should check that this design does it.
My guess is it wouldn't work with a 6VA transformer because the secondary voltage would've been too low. Mains transformers always have more turns than expected on the secondary to make up for the voltage losses under load. Even with an ideal 12V to 110V transformer and a 12V PWM sinewave, the maximum secondary voltage will be 78V which will reduce the torque somewhat. You'd probably get better results from a 9V transformer which will give nearer 110VAC with a 12V supply.