Before doing anything yourself, I would take it to the Apple store, give them a sob story, and if they don't help you, offer to buy Applecare if they'll swap the board out. I know many people who have done that successfully, especially for newer machines. It's worth a shot.
As far as cleaning the board, though, the instructions in that link look good to me. You basically just need to remove all signs of corrosion. Personally I use compressed air to blow away all residue, etc., after scrubbing with a toothbrush...there's less chance of doing damage that way than trying to use a vacuum and/or cloth. Also, I would disregard the part about taking apart the fan unless there is a specific issue, because you're more likely to cause a problem with it than have any benefit from preventative maintenance (although blowing it out with air never hurts).
I use 91% alcohol and have never had a problem. Sometimes it takes several rounds of cleaning before you get it all...a board has lots of nooks and crannies, so it's difficult to find all the problem areas at once. A flashlight definitely helps. And definitely take the board all the way out, because often there's more corrosion on the other side. Personally, I wouldn't take off the heatsync unless you specifically see corrosion in the area.
Beyond that, if you get as much alcohol on the board as I do, you'll definitely want to allow adequate time to dry before powering on. With 91% alcohol you're probably safe after a few hours, or overnight if you want to be 100% certain.