I like the idea but I think I'd lean in harder to this idea. The Twins should be positioning themselves to sell off the roster in July. It's clear this isn't a contender as constructed. The good thing about negative value veteran players is their value will go up as their contract goes down. The Twins have $50M in the budget. They should be trying to get the large market teams to give them prospects to take on high priced contracts of players they no longer want on the roster. The Twins don't want long-term commitments so they should be focused on players with 1-2 years remaining on their deal. You found one perfect player in Carrasco.
Here's a list of players with <= 3 years on their contract playing for teams with high payrolls who are probably no longer wanted by those teams.
Player Name Team years remaining $$ remaining
Josh Donaldson Yankees 2 $37M
Aaron Hicks Yankees 3 $32M
James McCann Mets 2 $24M
Carlos Carrasco Mets 1 $14M
Chris Sale Red Sox 2 $55M
Hyun-Jin Ryu Blue Jays 1 $20M (injured and not tradeable by the deadline)
Yusei Kikuchi Blue Jays 2 $20M
Tommy La Stella Giants 1 $11M
Scott Kingery Phillies 1 $8M
All of these players will be worth more at the July trade deadline than they are currently worth. Those teams may be motivated to give the Twins prospects to take them off their payroll.
Example trades:
Jasson Dominguez, Clarke Schmidt, Will Warren, Clayton Beeter, Donaldson and Hicks for Max Kepler and Trevor Megill
Carlos Carrasco and Matt Allan for Emilio Pagan