Admittedly just skimmed through the last 9 pages but I didn't see Mike Lodish mentioned. 10th round draft pick, career back up, until recently was the answer to the super bowl trivia question who played played in the most super bowls with 6 (Beebe played on 6 super bowl teams but did not appear in all of the games.) Tom Terrific just played in his seventh. Lodish and Lou Piccone are my picks, think those are the type of guys the OP had in mind.