The question I have is how fast is the content removed after the domain name registration changes, i.e., is there is a window of time between the appearance of a new robots.txt and the next scheduled crawl, and if so, is it be possible to "rescue" the content, as ArchiveTeam would do, during that window, before it disappears.

If this is possible, there could be a service for monitoring changes to domain name registrations for sites that have large amounts of historical content. I would happily volunteer to set up such a service.