Many thanks for suggesting this procedure and for having me go back to the Waters book :)
Personally, I don't think that using three decks (cough... six... cough...) will make the effect more practical, but I rather think will make it more cumbersome, that you will lose the "clean-ness" you have with Berglas' original method. Off the top of my head, I think you could use a single deck to be passed around the ladies, one each reversing a card, but this will require to have only (!) 26 balloons available, rather than the full 52. Is this acceptable? Perhaps it is... But the big problem with this is that you will end up with three reversed cards in the deck and you WON'T KNOW who selected which card! Yes, the three cards will still match, but you will have lost the partner-matching part of the effect. Is this something that can be lost? Or covered with some chutzpah? Not sure...
Anybody else has some idea to share?