The Giants were beneficiaries of two very lucky plays to win two recent Super Bowls. I wouldn't include them but everything else you said was correct.
Though the Rangers averaging a Cup Final every twelve years isn't bad.
Since 1950, the Rangers have been to 5 Finals. Yes I know it averages out to 1 every 14 years, but the level of incompetence the team has shown for the most part is staggering. They've won 1 championship going on 80 years. Luckily I was in attendance that night at MSG, as I'm not confident they'll ever win again in my lifetime.
I remember one lucky play for the Giants in the past 2 super bowl victories. The Manning to Manningham play was pure skill on both ends. However if you've followed the Giants the past 35+ years like I have, it's maddening to think of the ridiculous ways that team has come up with to lose games. Two shining examples would be Flipper Anderson & Plaxico Burress. I don't think I need to elaborate.
The Jets are an entity unto themselves. Their die hard fans have it pretty bad.