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The problem is that motors such as those are not built to slow down. They're meant to go at 1 particular speed only.
The only decent way to make them go slower is a frequency drive, and that costs...

Yes, that is another thing wort considering. The motor won't really notice, but frequency convertors work by taking 60Hz, converting it to DC and then reconstructing a sinewave of the correct...

The speed is set by the frequency. The voltage gives it power (not exactly, but close enough for basic understanding).
If you cut the voltage, you'll just take away power without reducing the speed...

No. A variac will not make it go slower. It will just make it burn out faster.
You need a frequency drive to turn the 60Hz into 30 or 20 Hz.