Sort of kind of my thinking
No matter what the Packers do with Perry, they will have a dead cap hit of $11.1 M to contend with. This is the remaining portion of his $18.5M signing bonus. If they don't cut him prior to 3/14, another $5,137,500 gets added to that as a Roster bonus, then a $400K workout bonus and a $5.2M salary.
If they can convince Perry that if he doesn't renegotiate his last 3 years, they will cut him pre 3/14, no Roster bonus and Perry is a FA. Remember, Perry already has been paid the $11.1M since it was a signing bonus, its just a cap number right now.
So depending on Perry's financial situation, health and outlook of his value on the open market, he would have to decide. If the Packers restructure the current contract as say a 3 year $18M contract (includes the $11.1 M already paid out), I make $6.9 M over those 3 years. Can I get that on the open market?
For the Packers, they get a guy that now only costs them $2.3 M/year. Which over 3 years is only $1.7625 M more than just his roster bonus is this year.
Obviously, the Packers have to determine if Perry still is valuable to them and what that value is and then hope that Perry agrees with them.