Route #1: Eat some salary and trade a lesser prospect
I'm not sure which teams will be in the market for an innings-eating, 36-year-old starting pitcher who isn't overly useful anymore this offseason, but there's bound to be someone who will.
Teams are always itching for starting pitchers. The issue is that this year's free-agent starter class is chock full of talent. Corbin Burnes, Max Fried, Justin Verlander, Max Scherzer, Jack Flaherty, and Shane Bieber are only some of the pitchers who will be available. The second tier of starters is equally as voluminous.
Trading an expensive pitcher in a free-agent market that is rife with more talented pitchers will be difficult, but it's possible. If the Cardinals are willing to eat some of Mikolas's hefty paycheck next year, they could save themselves some prospect capital. While this was to a lesser degree, the New York Mets took a similar approach at last year's trade deadline with Scherzer and Verlander. They received a prospect when they shipped out their pricey veterans, but the Cardinals will likely have to send a prospect due to the massive gap in talent between Mikolas and those other veterans.
Obviously, the more money the Cardinals send the lesser prospect they'll have to include. I would be content sending Mikolas with a prospect in the organization's #10-20 range, and this would likely require the team to take on at least half of Mikolas's salary.
These are educated guesses, obviously, but there is a track record of deals similar to this one in the recent past. The Dodgers traded a struggling Matt Kemp and covered a third of his remaining salary to lessen the prospect capital they would have to include. The Cincinnati Reds traded Homer Bailey to the Los Angeles Dodgers along with $7 million in cash to cover part of Bailey's contract.
The Cardinals could do a similar thing with Mikolas this offseason. They can eat some of his salary while also sending lesser prospects in exchange. By sending cash over to the other team, Mozeliak can also request a better prospect in return.