What I do:
Tuck box isn't involved in the switch. I have the extra deck sticking out of my pants in the back left, tight enough so it's held there fast until I need it. I angle my body so my left arm is almost completely obscured drop the current deck into my back pocket and grab the other one.
It's done quickly but naturally, and always offbeat and/or with misdirection.
It's probably been done, or something similar. It's pretty straightforward but it works awesome.
I use it to switch out the stripper deck.
If you heard it hear first and use it, credit please.