Doubtful. Starters generally have a more competitive market than relievers, which can necessitate a team commitment like Pineda's deal, and more importantly, shoulder surgery is very different from Tommy John surgery. It's much less predictable if and when Dyson will return to effective pitching.
Dyson will likely be looking at a minor league / incentive type contract for 2021.
Could be... but where is the point where the Twins (or any other team) would deem it an acceptable risk.
I'm sure Dyson doesn't want to go an entire calendar year without getting paid.
Sign him to:
2020 - $2M
2021 - $3M
That's probably a little more than is necessary, but that probably gets it done on Dyson's side. At that point you're competing against all 29 other teams, so a little overpay (if you want him) will likely be required.
You might get Dyson toward the tail end of 2020 and you'd have him for 2021. If Dyson gets fixed, then $5M is worth it. If he's not fixed, then you're lighting $5M on fire.