I was thinking of something that would work with a personal domain, with a mail server that I (indirectly) control.

It would maintain a small pool of immediately-available addresses, since there might be latency in setting up a new one. When I need it, one is removed from the pool, recorded with metadata (e.g. purpose, duration, who to blame if it gets spammed), and in the background the process is started to restock the pool.