I'm happy to say that I attempted this today and it seems like it worked! Thanks for the encouragement and of course the initial very-clear, very helpful instructions!
Is anybody in the Philadelphia area interested in performing this fix on my 2003 Protege for $200??
My wife has had enough of the AC only working intermittently and I'm going to have to move on from my beloved Mazda if I cannot get it fixed. I was able to pull out the radio and start poking...