I’ve tried all the “quick chill” methods I’ve heard of, but none of them work as quickly or as well as the icecream maker method. Watered down ice with some table salt. Set your unopened beer into a slurry like that, and in about 20 - 30 minutes, it’s surpremely cold. None of the “5 minutes and it’s ice cold” methods work as well or as quickly to be honest. At least not in my climate and in my experience.
There’s a cheap machine that dip the can in ice cold water and spin it really fast. It cool the can down to <5°C in less than 3 minutes. I think it’ll work even better with your salt method.
Edit: changed the time and temp because it works even better than my memory.
By spinning the can in ice water, it increases the rate of transfer of heat energy from the drink in the can, to the can itself, to the ice water. It’s like how stirring the ice in a cup of not-cold water will melt the ice / cool the water faster.
At a molecular level, you would see an increase in the number of collisions between ice molecules and liquid molecules. The collisions must occur for heat transfer to happen, so more collisions = more cooling. It is also the same reason why a heatsink can draw more heat from a processor when a fan blows air over it (until the air is saturated with heat).