If you are going to go with a direct drive setup with no gear reduction, you need a high pole count motor. Superior (Slo-Syn) makes single phase and 2 phase AC synchronous permanent motors with a shaft speed 72 RPM at 60 hz that can be speed controlled electronically with a VFD.
Here is some info on the operation:http://www.industrial-electronics.com/emct_2e_5i.html
They are very similar in construction to the Lyrec motor used on some lathes. They are better than a typical stepper as they have a sinusoidal winding distribution and so should have much lower torque ripple when driven by a sine wave source.
I'm in process designing a drive for this type of motor. I have a used Slo-Syn motor due to arrive to experiment with in the next day or so. I'll let you know if it works out to be smooth enough (low torque ripple) for this application. I am also looking at re-purposing a ceiling fan motor to drive a turntable. They are also high pole count single phase AC induction motors (not synchronous) and are available at low cost. If I get anywhere with any of this, I plan to post the results here.
Let us know what you end up doing.