I very nearly made the same error, buying a 220 version instead of a 120 one.
Just guessing here, I suppose the two differences would be that the 220 film is thinner than 120 film+paper backing, so the "pressure plate" might be tight. In the Mamiya 6, changing the setting from 120 to 220 is simply a small shift in the pressure plate's clearance to the film gate. And the other difference would be in frame counting, so maybe you could find a way to skip frames 13 to 24 if you were to give the 120 film a try.
At least with the SE backs, no longer does one rely on the film+backing+tape thickness to set the frame counter when loading, so that's one problem you wouldn't have.