If they didn't have to carry Lester's personal catcher, my opinion is the Cubs would be better off just keeping Montero and still moving Schwarber to C if can play there defensively. You won't get much for Montero in a trade because he isn't worth much more than $14 million, and a lot of the teams that can take on payroll are set at C. You could play Montero at C every 3 or 4 days to keep Schwarber fresh while trying to hide Schwarber in the OF with a pitcher like Arrieta on the mound.
The Rangers or Padres may be trade partners for Montero, though. I'd maybe try to trade him to the Rangers with a middling prospect, and get back Leonys Martin. That guy is a stud defensive OF who seems to have fallen a bit out of favor with the Rangers.
Anyway, that's just my outsider's opinion.