Without reading the whole topic, allow me to share my (similar) patter which I use with this trick, and I get pure success out of.
Like you, I also perform the Biddle trick second or third in my routine, with the excuse or after being asked how I do it, so I say "I can only explain half of it, but here goes".
I don't see any reason for you to suddenly give them half of the deck like in the original topic here, so what I do is use the conventional way of briefly checking a couple of packets that I cut from the top, until I get to the middle and narrow it down to 5 cards. My patter along this phase is "I can't scan through 52 cards, so what I do is scan through small packets really fast", and then I tell them I wanna make sure that I'm on track still and present the 5.
For the second part of the trick I have two variations, I'll start with my old one, and then the new one I adopted a few weeks ago which I highly recommend and which involves the audience outstandingly.
In my older method, I show the first card saying it's not theirs but it's like a clue and I just make something up ("this is low so yours was high, or this is a hear just like yours, this card indicates you had a black card" etc.), I do the same, briefly, with the second card, flashing it, the third I don't show and say something like "no... not the six..", and then the next card I don't show at all and pretend it is their card that I am looking at (after peeking it during the count in phase 1). I then hold it above the packet with my left and, and pretend to palm it with my right hand, just by dropping it onto the packet, and immediately perform so magical vanish (I patter with static electricity or a wavy shake of my hand while pretending to screw up the card like a piece of paper).
Note1 that during the showing of each card I return it to the packet to a random spot and pull the next one from a random spot, bottom, top, middle.. this is so they won't follow from where they saw their card in the count.
Note2 sometime during the clue patter phase I briefly ask them if they know what palming a card is, and say it's an old trick, show them how I hold a card in classic palm, and then on the offbeat say how "I'll show you something cool in a minute".
My newer way of performing the second phase of the trick, involves the audience much more and really brings them into the magic personally, plus is entertaining for everyone. I ask "who has the best imagination here and can help me out", whoever I pick is then instructed to "pretend to pull out one card from this packet, and now turn it over and put it in the middle of the deck, face up". During the instruction here I mildly demonstrate how these moves should be pretend-done, I added this in since one time before I did it this way, someone actually cut the deck, which is very risky due to the natural break from the face-up card. After the imaginary part it done I explain "you could have picked the *1st card" and name it, turning it over, second, third, and slowly also the fourth. Then you must pause and let the first step of the reaction sink in, they are supposed to know what's coming next. Then say "but you picked the *selection", and you name the card that was selected, if the audience might be a bit slow you can add also "and put it in the middle of the deck face up", but usally they know what to do next.
I have always gotten great reactions to the biddle trick, and highly recommend both of these versions, I dare not say they are perfect, but I have been tweaking this trick more than any other trick I perform. So give them a go, both versions, and see which works best for You.
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