I'm new to this forum, but I did like your handling of this. My recommendation would be to change the way you "pick" your sandwich cards... it makes it look like you have a marked deck, and if a spectator feels that... then they are going to think you are "cheating". They won't likely catch the slight, but they are "looking". You don't want people thinking you are good with cards, you want them thinking wow, how did that just happen.
You could start with your sandwich cards on the top of the deck... unrevealed. Then when your "move" is done, use the double to flip over the third card, and then turn the double over, sandwiching the selection, lift off and then do your reveal. The human eye follows large movements, so you could slow things down (which goes with your handling... very slow and "fair" to the spectator), but exaggerate with a larger arm movement.
Just my thoughts! Keep up the great work.
... Line