Hello, I don't know about the handling issue you seem to be having. I have an 06 XTX and it loves the corners, just had to get used to a different riding style from my sports background. If the tyre pressures are OK and they are not badly worn I'm not sure how much of a problem it would cause unless you're really pushing the bike, I've never run an over sized tyre so i couldn't tell you about that.
You could think about treating yourself to a new matched pair of tyres and give yourself some time to get used to biking again. Gain some confidence back and get used to the bike.
The surging low down at low speeds is known annoyance on an otherwise great bike. You have a few options and a good place to start is here, with our resident guru Kev
http://www.xt660.com/site/node/53
Adjusting the CO setting is the first and easiest thing to do. After that doing some mods that will help the engine breath better will help including
1. Remove the airbox snorkle
2. Drill the airbox
3. Fit a DNA stage 1 (and maybe stage 2) air filters
4. Make or buy the Kev mod to adjust your fueling if you have the DNA filters
5. Buy the more expensive and much more customizable option up from the Kev Mod, a power commander
Take one thing at a time as you can afford them and see what improvements you get. Loads of information is available on all of these options on the site.
And Welcome