Is there a complete list of NES games out there with a battery backed save? Every single one I've come across on the internet seems to be missing a lot of games that I know for a fact has the feature.

It works.

Easiest: Buy a new 360.
Cheapest: X-Clamp
Best: Reflow.

There is a screw underneath that sticker. After you unscrew that, you should be good to go.

It works fine for Mario but it screws up the other two.

possibly, but all you have to do to play SFC games in a SNES is break off a couple of tabs in the cartridge slot. Easy as pie.

"Would you kindly?" -Bioshock

It mentioned in the text for Zelda that the games were voted on so there is probably bound to be some disagreement.

HTC Tilt

Super Mario 64 DS, and I think someone one here was selling a copy for 5 bucks. Maybe it's gone, I'm not sure but I'm pretty sure you can find a copy for less than 20.