Wouldn't the first application of the swirl remover do more of removing your last coat of wax rather then working on your clearcoat, leaving you to go over it again? That's what I am thinking, and it seems like wasted product to me.
Also, if you are going to use something like Dawn to wash the car, wouldn't hot water be best to use? I seem to remember a discussion, and it being said that hot water is 'harsher' on wax, speeding up reactions between wax/paint.
Seems like a hot Dawn wash would do a number on the wax, maybe even through in some Simple Green, you would have one nasty car wash...