Summary so far:
**** Butkus (LB Bears): 1st ballot Hall of Famer, 8-time Pro Bowler, 5-time All-Pro
Gale Sayers (RB Bears): 1st ballot Hall of Famer, 4-time Pro Bowler, 5-time All-Pro
Larry Wilson (DB Cardinals): 1st ballot Hall of Famer, 8-time Pro Bowler, 5-time All-Pro
Dan Dierdorf (OT Cardinals): Hall of Famer, 6-time Pro Bowler, 3-time All-Pro
Roger Wehrli (DB Cardinals): Hall of Famer (vet committee), 7-time Pro Bowler, 3-time All-Pro
Sonny Jurgensen* (QB Eagles/Redskins): Hall of Famer, 5-time Pro Bowler, 3-time All-Pro
Don Majkowski (QB Packers/Colts): 1-time Pro Bowler
Bert Jones (QB Colts): 1-time All-Pro
* Jurgensen was on a championship team in Philly, but only as a backup.
Some things to note here:
All of the serious contenders here played most of their careers before the 1978 expansion, when the second wild card was added. Before that there were a lot fewer playoff games and thus a lot fewer opportunities.
The two on the list who approach Gonzo's stature are Butkus and Sayers; none of the others would be considered one of the best of all time at their positions.
It is interesting that the Bears, with one of the best linebackers of all time and one of the best running backs of all time, did not make the playoffs at all. In 1965 they had the #2 scoring offense and #2 scoring defense, yet finished 9-5 and missed the playoffs. That might be one of the best teams to ever miss the playoffs. Other than 1965, Butkus and Sayers had only one other winning season (7-6-1 in 1967), and in 1969 they went 1-13 together. In Sayers' two best seasons, 1966 and 1969, the Bears won a total of 6 games.
This analysis actually brings my opinion of Sayers down a notch.
Both Sayers and Butkus had their careers prematurely ended by injuries; it's possible they would have had a chance to win a playoff game had they played longer, but considering how bad the Bears teams of the early 70s were (they had no season with more than 6 wins from 1969-1975), it may not have happened.
Unless someone comes up with another name, it does look like Gonzo is kind of in a class by himself, at least in terms of careers since 1978. He's still playing at a very high level, so if his situation improves, he has a few more years to get that elusive win.