Since we are talking about hare-brained ideas, if my coke is flat, can I
put a bit of dry
ice in it and recarbonate it if I screw the lid on?

Tried it, doesn't recarbonate it. I dropped a tablespoon or so of powdered
dry ice into a 20 oz glass about 2/3 full of Coke. Got lots of bubbling and
fizzing and a cool fog rolling off the top - it was definitely worth it when
I walked outside to sit for lunch with some fellow students back in grad
school :-). Problem is you need the pressure to drive lots of CO2 into
solution to get the proper amount of carbonation, the dry ice wasn't nearly
enough at atmospheric pressure.

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Regards,
Carl Ijames