For instance, one simply needs documented evidence that 1) the right populations were clearly made aware of vaccine location and time, 2) communications went out to "in-scope" target audiences at least X hours before the doses expired, and 3) if vaccines are at threat of expiring once they are - let's say - two hours from expiring then those that control that particular supply should do everything they can to use them.

And while this solution is a bit reductive, it's honestly not that reductive; this is a solvable problem. People on Hacker News solve much, much, much harder problems than this.

And I'd rather 20% of vaccines go to the wrong people than 5% of vaccines go in the trashbin, personally.

How? If X people made appointments in a day, then exactly X vaccines should be distributed for that day. Leftover vaccines will only be distributed after all those appointments are over, so it is impossible for any of the X people(assuming they arrived on time) to lose their vaccine.