Heresy, I think, but one "big name" that could be shopped would be Contreras himself. With his bat and arm and power and youth and energy and club control, he could be really attractive player for a team that has a catcher issue and has no solution in development.
Wouldn't make much sense for Cubs, of course, since then they'd lose an asset. But, what if they think he's a nut and that his pitch-framing and game-calling is really a significant liability, and that he doesn't provide the leadership often associated/expected from a catcher? If you were to replace him with low-$$ guys with with more experience (even if you cobbled together some solution from among Avila, Rivera, and Caratini, you might not be awful at catcher. But you might be able to get a WAY better pitching package in return for Contreras than you could ever dream of for Happ or Schwarber.
I'm not advocating, just trying to think outside the box!
Sometimes it's hard to guess how much value Cubs might place on pitch framing, or leadership. Without which it's hard to estimate exactly how valuable a player is or isn't.