Kudos, Stinkypete, for doing a good job of considering the numbers in your thoughts. I'll build off your framework to comment where I care to.
LS Danny Aiken He can be signed cheap with minimal guaranteed money. Sign him and some camp competition and see how it falls out.
DE Akeem Ayers He gets paid more elsewhere. Assuming Mayo takes a restructure, Hightower would provide the depth needed at rushing DE/OLB.
DT Alan Branch Probably let go in favor of a draft pick, unless there's a hang-up with Wilfork. Wilfork's situation will be resolved one way or the other before FA, so this is an easy decision to defer a month.
LB Jonathan Casillas. Agreed. He gets the BB star STer salary that can't be found elsewhere - maybe $2M.
OL Dan Connolly. I think he walks. Someone else will offer $5-$6 million.
He's not getting that much anywhere. I think he gets a one year deal commensurate to last year - $3M with <$1M guaranteed.
K Stephen Gostkowski. Signed for 4-5 years at ~$4M per. The value is there.
S Devin McCourty. Franchise tag
Disagree. That cap number is too high and makes it harder to resign him next year, as his cost will go up. I think they come in just shy of the franchise level ($35m/4), such that the cap hit this year is lower (~$6-7M) and it escalates with the increasing cap in future years.
RB Stevan Ridley. Vet minimum deal with modest bonus for a team player. Probably 1 year, although it could be 2 years, if the injury is bad enough that he isn't expected to have much of a chance to prove it this year. This would be a case of paying cash to a team player but not hurting the cap.
DT Sealver Siliga (restricted). Also a no brainer at RFA money. I think Siliga gets extended long term post draft.
Agreed, although I think the timing of an extension will be during pre-season. He is worth locking-up before his value goes up, if he doesn't want to take a chance and hold-out for more later. There is probably a good both side value proposition at $6M/3 with $1M guaranteed, if the funds exist.
RB Shane Vereen. This is a RB that the market is primed to overpay. I think he gets an offer he can't refuse from a team like Indy.
Agreed. James White gets his shot, unless one of the defensive contracts falls apart. If Revis walks or Wilfork get cut, due to an unwillingness to restructure (I'm convinced Mayo will restructure), Vereen can probably be signed for $18M/4.
Revis. I have the feeling he will stick around for a few "1 year deals" and jump ship as the Brady/Belichick eras come to an end. $14 million will keep him.
I think you have the average dollar value right, but Revis took his chances with injury this year. He's not signing for less than $42M/3, and I'm betting he'd lean toward $52M/4 or more.
Wilfork. I don't see him taking another pay cut after last offseason. I don't think they'll be ready to consider cutting him for another year.
Agreed on Wilfork's side, but I don't think the Pats will accept a $9M hit for him. Unfortunately, I don't think he has a lot of mileage left, so there is little room to negotiate. He's due $15M/2 years with $4M guaranteed in a month. The only space I see for a deal is around $18M/3, but Vince may not want to play that long at that price.
Mayo. Mayo has very little leverage given the 2 season ending injuries and emergence of Collins and Hightower. It's his turn to restructure, and I think he does it. The defense is much better with him.
Agreed. He's not going to get top dollar after his injuries, and he's more valuable to the Pats than anyone else. He's going to have a much reduced salary with incentive clauses for this and perhaps future years.
Arrington. Arrington stays. I think he is paid to his value. He's the best slot CB they have. If he gets cut, it's because Dennard, Ryan, and Butler all show improvement next pre-season and somebody steps-up to take his place on ST. I don't see all that happening, but there's not enough near-term cap savings to make it worthwhile to cut ties with him.
Amendola. I think Amendola has earned his place on the offense. Something clicked on in his game in early December and he was an essential piece to the playoff run.
Browner. I don't see a better option at the money.
Agreed on both, but I think Amendola is in line for a pay cut. There's no bonus due this year, so the negotiation can wait until we see whether Dobson, Boyce, Tyms or a new guy take a step up next year.