Is the card lost in the middle first?
if it is then give this a try.
hold a break above the chosen card. show the bottom and top cards of the deck. then say that the card is lost somewhere in the deck. as you say that spread through the deck to kinda show that their card is somewhere in there. then, cull their card to the bottom.
yea, thats kinda impractical. you could also try the glide.