That would be cool to see. And very different from the usual dancing you see in those competitions. I imagine trying to tap in modified footpaws would be insanely difficult o.o
I think the footpaw rule came about because a lot of dancers were starting to move to those large plush-style sneaker things. And in typical furry fashion, drama ensued because they're 'easier' to dance in than actual footpaws. Or something like that. One alternative for you would be to participate in the variety show instead. You could wear your taps with the rest of your suit and not have to worry about the silly competition footpaw rule. Though you also might be able to style a special footpaw for tapping that would basically be a cover that rests over the shoe, but your actual tap shoes would be what contact the ground beneath.