Or maybe you should just stick to the original, because in fact I don't really see the logical point of the back changing. I agree that it's magical, but to me it doesn't relate to the rest of the trick. I think the Biddle trick is very well structured : starts like any pick a card trick, then the magician "fails" to find it, and then overcomes the difficulty by doing something completely impossible : you teleport their card from your hands to the deck they've been holding the entire time. What would be the point of having a different backer here ??
In Strong Magic Darwin Ortiz talks about "twists" and "extra kickers", and to sum up he says that if it's not completely logical, or stronger than the original climax, or confusing then don't do it ; I think that making smth appearing in their own hands is stronger than showing that the card has a different back, plus I'm affraid it adds confusion : in the original ypou spread the deck face up, and then there's this face down card => "wow, could it be...?" (builds tension). In this new version, it's more like "wow, could it...wait, it's a red card ? Where does it come from ?"