Look across the hallway for some pointers. The Giants have been responsible for more Super Bowl misery than I cared to endure the last few years, but I at least respect them as an organization. Same goes for the Steelers, Broncos, Packers, Colts, et al. in other sports.
You're lambasting the Jets for being a poor organization, and point to 5 of the last 6 teams to win a Super Bowl as model respectable organizations? Of course they're model organizations, they've had recent success!
I would say a better analogy would be teams like the Texans, the Titans (up until Jeff Fisher leaving) or the Ravens would be better role models for the Jets. The Broncos are probably the team you were looking for, as you mentioned. All teams that have overcome adversity, had some playoff success, are looking to get over the hump, but don't throw their players under the bus. The way the Broncos handled the Kyle Orton benching was classy (and they way they dumped Cutler was classy, too). The way the Jets are handling Tebow and Sanchez, plus signing Braylon Edwards after he shits on the GM is not classy. The way McElroy admitted in an interview that the lockerroom is dysfunctional is not classy.