OK, here's what I suspect, though I could be completely incorrect.
First of all, there's no tricks with cutting the glass, working with preformed half-bottles, etc. They're genuine full-blown glass bottles, decades old in most cases. He uses fairly wide-mouthed bottles, though certainly not wide enough to fit an entire deck.
I've heard that ship-in-a-bottle builders who weren't doing the bottle cheat built their ships a piece at a time, using intricate long-handled tools for doing the assembly work. I think he does the same thing with the cards. BTW: ALL the AIPs I've seen photos of have their cellophane intact!
Start with a deck, either sealed or with a spare cellophane seal of the correct size. Remove the seal if it's on the box, retaining its integrity. Carefully open the deck, either gently folding back or completely removing the deck seal (if replacement seals are available). Remove all the cards and open the box bottom, allowing you to flatten the box.
Gently curve the box so as to not leave a crease. Use tools to insert it into the bottle, then reform it and glue it where needed. Once the glue is dry, insert the cards one at a time into the open box, using the same gentle curving to get them into the bottle. Any residual curvature in either the box or the cards becomes unnoticeable/removed as the box fills to capacity. Apply new decks seal (or reapply old one still half-attached to box).
The trickiest but not impossible part is re-wrapping the box in cellophane, but if a doctor can remove cartilage from inside my knee or bone from my shoulder while leaving a scar smaller than a dime slot, I don't think for a second the tools to do this job don't exist. Cork it and pretty it up to specifications. Voila, one AIP bottle.
That how I think it was done. At the least, it seems the most possible way to do it, given the restrictions of using a non-gimmicked bottle.