Jax would be wise to hang onto him if they can. Whether he's a starter or a backup is up to him. If it's really an open competition for starter and he wins it he's the man.
It will be interesting to see if Jax will start Sunshine game 1. I guess with a new coach and offense to learn the QB's are on a level playing field so to speak when it comes to the play book. Minshew has a slight edge in actual NFL experience.
I don't know if they're going to get him signed. They're playing games with his contract with offset language and bonus payout dates. All the precedents are working against them but they're evidently dug in. Wilson's family isn't exactly hurting for money. If there's someone positioned to give them double middle fingers and just re-enter the draft next year, it's this guy.
Long story short, the names and faces in the organization might change but the Jets are gonna Jet.