On the Slack SSI general chat Ice used the term "make a path" as a way of describing how the M's should approach dealing with a broken Felix, who has one more year on contract at about $27 million. I like that phrase as a guideline. You present Felix with as generous a path as you can, one that preserves his dignity as best you can. If Felix takes it and acts the part, good. If he doesn't you have a plan B that is not as attractive to him or to you.
The cost of Felix is sunk. Even a traditionalist like me understands that. You have to decide if he's a potential asset in any capacity. If you decide he isn't, what good does it do to leave him on the roster and drag your club down?
Me, I'd find some way to swing through August (find some ailment that justifies a 10 day DL stint that can be extended, or some such thing). Then when rosters expand in September you can carry him without the need to pitch him except in blowout losses. There is no need to DFA him now UNLESS, as you say, he behaves in such a way as to be a negative influence in the clubhouse.
Then I'd give Felix the offseason to prepare for a spring that will be make or break for him. I'd also add pieces that can pick up his innings if he can't cut it. If he buckles down to prepare for next season and shows enough to consider him a fifth starter or better next spring, you keep him until he proves otherwise. If he doesn't, you DFA him then.
Oh, and I'd also try to find a way to have a couple of conversations with key players about the situation. Not that you let the inmates run the asylum, but you have the potential for treating him this way being even more of a negative impact on the clubhouse than a "bad attitude" Felix. The "guys" have to weigh Felix' negative impact on their pennant chase vs. their loyalty to and respect for The King. Frankly, it's the same dilemma the fans, the GM, and the manager have.
Edited to add:
It goes without saying that you offer Felix an honored "Mariners Ambassador" position with the club. This post is more about on-field matters.