Plymouth, WI
Yup...we've all been there! I will still sometimes do bulbs with the game on, but make a judgement call based on where they are. I know damn well I'm taking a risk doing it though...LOL.
For removing the solder, all you really need is one of those simple solder suckers. The cheap/dirty bulb (turkey baster) style works fine for occasional board work. I always meant to get something more fancy, but haven't found it to be really necessary yet. Give it a shot...you can't make it too much worse than it already is (well...for the most part...) 
