Well, I solved it. More or less. This may be of interest to the plugin authors. Basically, every instance of the root domain verbal.ee had been replaced with verbal.ee/yogin/yogin (with the latter being doubled). This created all the login problems. When I searched and replaced those aproximately 1600 occurences in some 12 different columns I got all my websites back. In addition, the database for my main WP install at verbal.ee had been completely dropped, it was erased. So that is why the “infamous 5 minute install” was being displayed – it looked like a virgin WP install.
The only downside was that for some reason one of the online shops I was building had forgotten all sidebars and style settings set via MayaShop themes special theme options. Not a trace of that data in the database. But I’m pretty much back up and running. And on to make backups, backups, backups. That was a traumatic close shave. Learned to work with databases better, which is a good thing, I guess. I’m reluctant to use the plugin again, though. Some comments from the authors would be welcome. I will be happy to provide more details if needed.