Long time reader...first time poster with some thoughts:
I agree with the posters of tweaking the roster, but not blowing it up unless there is a significant losing streak or drop essentially out of contention. Adding a RH batter and especially a bullpen arm (or two) to bridge the gap to Stewart (when back from IL), Jax, and Duran. That answer might be Balazovic if FO is willing to use him similar to a pre-starter Liriano or Santana, but they seem reluctant to do that with any of their starters in St. Paul or maybe the starters there are not capable of doing that type of work in today's baseball. We cannot sell the future for now since now, even in its best iteration, isn't going far in the playoffs.
I will preface this by saying I am a fan of the SEA/NYM trade where Seattle dumped Flexen onto the Mets and let the Mets DFA him. (Hint: That might be the best way to get rid of Kepler, who I believe is still a fan favorite)
Let's take a full analysis of each player expected to be a free agent at the end of the year and see what we can actually get. I used Sportrac as my research. Minnesota Twins Multi-Year Payroll | SpotracMinnesota Twins Multi-Year Payroll | Spotrac
Sonny Gray: Best to ride him out unless you get blown away by a deal. Everyone says he is gone after this year. He has injury history. There is no reason to think that the FO wouldn't try to resign him considering the price they paid to get him.
Joey Gallo: DFA candidate as soon as we get reasonably healthy.
Max Kepler: see my hint above for a creative possibility. Definitely not take the club option for next year and set him free. Otherwise, use him as a defensive replacement for Wallner, Kirilloff unless someone really wants him.
Emilio Pagan: Why is he still here? He makes me dream of the Fernando Rodney Experience.
Kenta Maeda: See what he has prior to the end of the year. He should be flexible as starter or even an opener. Unlikely to trade him since he is just back from the IL and still coming back from TJ.
Donovan Solano: Possible trade candidate due to positional flexibility. Either looking for a lottery ticket or BP depth in return. Likely not hitting enough to trade.
Micheal Taylor: You need him as long as long as Buxton is doing his DH impression. Celestino is not ready, Nick Gordon doesn't seem to be as comfortable in the OF, and neither seem to want to steal a base.
Tyler Mahle: No reason to resign him unless you get a dirt cheap contract and can stash him.
As you can see, there are not a lot of expiring contracts that any other team is going to want or that we will get any reasonable value in return where that player is not more valuable to us. Any of the more expensive ones (Gallo) is going to require the Twins to eat a lot of the contract, which they have never been a fan of doing.
Other players mentioned on here have been:
Vazquez: 2y/20m - again unlikely unless you get some team to take the salary. Probably better developing an emerging pitching staff.
Polanco: He seems to be the player, when healthy, that can actually get the offense going. I'll grasp at straws until Julien can secure that role better than he is now.
Castro: There is a push to want to trade him since he has never done as well as he is now. His positional flexibility is the only reason that we can still fill out a lineup card every day. He is still more valuable to us than anyone that we would get back in a reasonable trade. Heck, he was originally only on the roster to be this year's Billy Hamilton and I think he has exceeded expectations.
We still haven't discussed Dobnak or Paddack, which are total wildcards and will need to be assessed whether they are worth a 40-man roster spot as prospects keep moving up.
This was a much longer post than I ever intended and probably should have been it's own thread. I hope to see the Twins this weekend and ever eternal that they will turn the corner.