I made my layout before noticing that there seems to be no good way to get the analog triggers to work. Luckily, SFII only needs 6 buttons. So I'll be going with a more traditional 6 button layout, unless I can think of something to push the lever.
When I get home tonight, I'll take a few photos of the dissected pad. I've heard the thing about the black stuff over the contact, but this 3rd party controller just has a square rubber pad with 4 "columns" to make the contact. I don't think I have to scrape anything off as the contact is gold.
Thanks for the tips. I planned on making some practices and hopefully not heating the pcb for more than 4 seconds at a time. Would that be too long? I've read 2 seconds with just the iron, about 1-2 seconds of solder + iron, then pull the solder away quickly followed by the iron. If I screw up, at least it was only a $25 3rd party wired pad instead of one of the $60 MS Wireless ones.
It's generally "two seconds", but as with everything, there is a little leeway, I guess. It also depends on how hot the iron is, but you generally shouldn't be using anything higher than 45w on things like this, especially at the beginning.
If you've just bought the iron, and if it's a cheaper iron, then you'll want to make sure you tin the tip of the iron when you first plug it in. Wait around for it to heat up, pressing a bit of solder to the tip every so often. YOu want to coat the tip in solder to protect the tip from corrosion. A black or deep brown tip has oxidized and will not transfer heat nearly as effectively as a golden/silver tip. Having a tip that is in good health will make your joints that much better and you'll be able to get in and out more quickly.
I would try to have small (reasonable) amounts of solder on the tip when you go in to make a joint. The excess solder helps to make sure you're making contact with both surfaces and helps transfer heat more quickly.
Just like painting, or cutting wood, there are signs to look for in a joint to tell if it's good. You generally want just enough solder to make the connection. You should see a concave blob that bridges the empty spaces, between the wire and pad, for example. The joint should be shiny and smooth, as opposed to grey and pitted. The latter means that you have a cold solder joint, and while it may not be overly critical in this sort of application, there is no reason not to do the best job you can, right?

A cold joint may work right off the bat, but it may suffer from intermittent connections later on in life, may not be structurally sound, and may just not work at all.
It's pretty common to give a little tug on a joint after it's cooled completely to test it's strength (which should be fairly strong), but try not to pull the pad right off the board...

Sorry if I'm rambling.