You should have stopped while you were ahead.
You point out the very formula for sustained success in the NFL. And I promise you, it aint by acquiring a 33 year old QB.
The Jets already have in place an OL/running game that is among the best. Factor in a defense that was good and only figures to get better. The Jets mix of draft/FA has done wonders (Mangold, D'Brick, Faneca, Woody, McKenzie comes back?). Young drafted talent at RB and TE (Keller, Greene). Decent/good WRs (Cotch, Edwards).
Then they make their move for whom they thought will be their franchise QB. In comes Sanchez. Because everything else is in place, Sanchez doesn't have to be brilliant. Yet he figures to get better with each passing season. If he becomes even remotely stud-like, look out.
Foritfy your lines, both O & D, bring in players to fit your new defensive scheme and let them become your calling card. The city we play in, the fiber of the people of Buffalo, should be demonstrated by the Bills defense every single Sunday. That is to say hardnosed and passionate. Then go find (draft) who you really believe can QB this team for the next decade.
Quick fix? No such thing for a perenial loser.