Hi Eudimorphodon!
Sorry I'm so late to the party (again), I've been catching up on a bunch of other stuff this weekend.
Sounds like you're making some progress, at least! I have a few words of advice about desoldering if you do want to go down that path.
Number one, it's incredibly important to have a good temperature controlled soldering iron for desoldering. A simple plug-in solder pencil or (God forbid) solder gun is absolutely, 100% not going to work
As you've discovered, they just scorch the hell out of things. They're not cheap, but you can get a totally reasonable temperature controlled soldering station for between $80 and $150, and they should last a lifetime. I've had mine for 15 years now, moved it across country three times, dropped it down the front steps, and it's still going strong
Hakko or Weller both make awesome stuff.
And number two, flux is your friend! I can't emphasize enough how much of a difference it makes, it's night and day. Get a jar of brush-on liquid flux or a syringe of flux paste and apply it liberally to both the solder side and the component side around each lead. It'll smoke like crazy, but that flux is going to help the solder flow so much better when you're removing it. After the component is out, you just need to clean it up with some alcohol.
Number three is your choice - solder sucker, desoldering braid, or both. I use both. I like to use the solder sucker first, and then the braid for touch-up. I really like this guy's video on how to use a solder sucker, he looks like he's really experienced:
http://www.youtube.com/watch?v=Aw4lZGk90i4
If you practice a little more, I think you'll find you can totally do it.
-Twylo