Great post @DocBauer! I want to flesh out a little more on a couple of your points.
Banda would be an arm I could see the Twins try to keep around. The Twins have shown a willingness to keep bullpen arms they consider cheap, see Topa last offseason. Finding any kind of effective LH RP seems to be hard to find. Even if you believe that Rojas will come back, I think you should have two good lefties in the bullpen. Rojas may need some work in St Paul though has his first rehab appearance didn't go well last night. Hopefully, one of Rojas or Funderburk will step up so we shouldn't have to resign Rogers. He has been a good teammate, but he just seems to be done.
Gomez is an interesting thought exercise. You want to keep him since he has been the only consistent reliever we have had in our bullpen this season. His overall body of work suggests that you may need to trade him while you can still get something for him. If he keeps it up, someone will overpay for him. Heck, we traded for Trevor Richards before so anything is possible. I don't see a huge payday for him, but if you can get a high A or AA flyer, that would be a decent return for someone you claimed off the waiver wire.
I agree with you about Clemens. I think he is one of those players you keep. IMO, he is a better version of Kyle Farmer. Speaking of Farmer, the Twins brought him back for $6.3M. Clemens won't bring nearly that much in arbitration. He should be worth the price for a solid player that can plug and play nearly anywhere. Clemens has taken the Willi Castro role and forced himself into the lineup every day and I'm not sure he brings back anything of real value in a trade. Hopefully, he can keep the young guys motivated as they know that Clemens is behind them ready to take their job if they falter. I think you can have two utility bench players if you pair him with Kreidler, who can play SS and CF as we will always need a CF option to play when Buxton gets a day off from the field.