Could Derek Carr be a post-June 1 cut?

A lot of people (including myself) think/thought a post June 1st cut saves the money off the cap immediately when processed. False
The team would have to carry the full cap charge ($50.1 million in Carr's case) until June 1st, the team would still have to cap compliant early March (already $63-65 million over). Getting under the cap without including Carr in March is unlikely.

The dream scenario is that a team Carr covets (more ready to compete) will be willing to pay his base salary $25-30 mil if he is available. If that happens Carr can agree to a significant pay cut (lets say $4 million guaranteed as a sweetener). Saints can then designate him as a June 1st cut saving $26 million this year and not having to push that money back into future years.

Without something unlikely like that happening expect a restructure to get under the cap.