I strongly doubt any of those 3 will be traded personally. You're not going to find a pitcher who's as useful as Q is for the price he's getting paid. Russell has no value. And I've said all I need to on Schwarber. I think they will likely have to package Happ or Monty with Chatwood to rid themselves of that for luxury tax purposes.
I still think Martin/Giles for Chatwood/Happ makes a lot of sense with potentially some lessor parts also being involved. If the cubs can make that move there's not a ton more I'd do. If they can't, I think you can make similar moves with other players to effectively get a closer and a back up C with good framing ability while also ridding yourself of Chatwood. I'd bring back Chavez. I'd bring back Hamels. And I'd sign Machado if I can and if I can't I'd probably try to sign Donaldson or Moustakes. I'd keep Russell at the very least until the trade deadline next july. You're not going to find his kind of talent depth to replace him and you're not going to get value for him so trading him really would be just spiting yourself to save face in PR. From there there's maybe some moves around the edges I might make but I think that's a fairly solid team. You'd have something like...
OF - Schwarber/Almora(quasi-platoon), Heyward, Zobrist(or Bryant)
IF - Bryant(or Zobrist at 2B if Bryant in RF), Machado(or Donaldson/Moustakes), Baez, Rizzo BENCH: Russell(Bote until May), La Stella
C - Martin, Contreras with potentially Caratini in AAA
SP - Lester, Hendricks, Darvish, Hamels, Q
RHP - Morrow, Giles, Strop, Cishek, Chavez, Edwards,
LHP - Monty, Smyly
You'd also have Kintzler/Duensing under contract for ST though I'm not sure either is ideal. Regardless, that's a fairly deep team. And you're not really having to do much fiddling to make this happen. Hamels/Chavez already have said they want to come back. The cubs will be one of the favorites to sign Machado anyways. The biggest speculation on my part is probably the cubs going after Martin/Giles. But, as I said I think it makes a lot of sense for both sides and even if the trade doesn't happen exactly how I outlined I think you still can package Happ/Chatwood some where and come back with the very least a half decent reliever. And there's other good framing C out there that wont cost and arm and a leg.