Okay, good news! The MariaDB is running off the RPi3B+ and the read performance off the SD card is not bad actually.
I did a full export of the MySQL database and imported it successfully into MariaDB using MySQL Workbench (which was moaning about unsupported SQL versions, but whatever).
The one bump in the road now is the "Recently added episodes" section for TV series, which has the all-known rotating wait cursor for about a full minute (will time it better next time) before those thumbs are shown. I have no problems with this on the PC when connecting to a proper MySQL server. All the other sections on the home screen load pretty much instantly. Also I now have a 45-second freeze when closing Kodi on the PC. No idea where that comes from.
vpeter Can you enable a log file for the MariaDB server?
There are the expected micro lags in handling database data when using a "big" PC or a "small" RPi device, but so far if you just blink once, you wouldn't know the difference when using the sql database on the RPi.