There are alot of different methods, I like your thinking....Quick, Easy, and well, Safe!
I rescued a chicken with a really bad case and this is what I did. It only took one round and it was GONE!
First I bathed and soaked the chicken (you could just do the legs and they LOVE it!) in an herbal flea shampoo. I used a tooth brush and lightly brushed her feet and shanks. This does 2 things: softens the skin and loosens the mites and mite dirt, then it treats the area to help it heal.
Next I put Campho-Phenique on her legs, completely covering her shanks. I also treated all my other chickens with the Campho, just in case.
Now that really took care of it, but I re-treated with the Campho in 10 days and then 14 days after. Just to be sure.
With this method there is NO egg contamination.
GOOD LUCK!!!
did you have to clean out the coop as well?