I agree that you'd need a transform to bring about the effects of the Mule's mental powers. No one ever "recovered" from the absolute loyalty he created, and no one changed by it had any chance of resisting. It would also be fully invisible - only detectable by the changed actions and attitudes of it's victims.
That said, he did seem to have lesser powers of influence as well - as when he demoralized entire planets into not resisting his forces when he was working undercover as a musician. For that i would suggest more conventional Mind Control with recovery bought down a few steps on the time chart, with a large area effect, perhaps even megascale.
As to Comps, yes, Secret ID at first, morphing into Public ID later, Distinctive features, probably Reputation. I seem to recall he overemphasized his hunchback when undercover, and could actually move well when he wished to, though like you I haven't read the books in some time. Perhaps a psychological obsession with the Second Foundation, a dose of megalomania?