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Beyond the PR ratings used by amp makers, Class D amps would be ideal for this application.
On a Class A/B/AB/C amplifier, the transistor is almost always in its linear range. Picture a monkey with a rheostat. You pull on the monkey's tail (gate or base) and he changes the resistance, and the amount of current through the circuit. The problem here is that the monkey's pot is always dissipating power that you wanted to drive the load. I expect your amp will end up pretty hot if you go this way.
In a Class D amplifier, you alternate between yanking on the monkey's tail so hard that the rheostat is zero ohms or that it's essentially open. The MOSFETs in a Class D amp are driven only into saturation and cutoff, so they aren't dissipating any power (oversimplification, but almost true).
It SHOULD work with any class, but I wouldn't try it at high power. I'd also see what varying amplitude and frequency did to your motor. AC control logic is way complicated.
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In theory, theory and practice are the same. In practice, they aren't.
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