Well, personally, I like using mics to amplify taps during a tap dance routine. The sound of the taps is an
instrument and should be mixed into whatever
FOH sound there is - PCC's work great for that. I remember working once with Michael Flatley when he was touring with the Chieftans - we spent quite a bit of time working out the mic placement so the taps would get picked up effectively.
As for the original question, seems to me that the director probably hasn't worked much with body mics to be worrying about excessive pick-up during tap numbers. And if for some reason there was a problem, that is what volumes and mutes are for. The advantages of using body mics for such a large undertaking as 42nd Street far outweigh any minor concerns such as potential dance bleed. I would get together with her as soon as possible to see what is available in the budget for mics - then you can start trying to put something together. There are many different ways to do it, but be warned - borrowing and piecemealing differents systems and mics together can be a real nightmare. If she gives you the go ahead, I would figure out exactly how many mics can be gotten by with and then contact local rental companies and check on the cost to rent units that will be frequency matched with the same mic capsules - your life and the ultimate sound quality of the show will be a lot better.