Screw all that complicated crap. I have cleaned thousands of keys.
Get some powdered laundry detergent, I use Charlie's (from Whole Foods/Fresh Market) the best for your laundry, too, by the way. A spoonful of that, along with a half a spoonful of Biz or Oxi-Clean (also very useful for your laundry) and, as another optional final touch, half a spoonful of washing soda, in half a gallon of hot water, soak the keys for 10-60 minutes, rinse 4 times in a colandar, and toss them onto a towel to dry.
If you are in a hurry, hand shake each one to remove the water from the inside.
0.1% of them may require something else. Try a pencil eraser.