WetGeek I can instead spend my efforts on solving the frequent re-scanning issue
It turns out that frequently re-scanning isn't an issue. The default conditions for the Elisa settings are like so:
For a long time, I left all those defaults in place. I'm now pretty sure that it's the Keep running in system tray ... setting that causes the problems.
If I turn that OFF, I can shut down the app and restart it numerous times without losing the loaded collection. The gear icon spins for a while, but it's just a quick scan to see whether anything has changed. It's not adding any tracks, because I haven't ripped any new CDs. It did remove some "Unknown" albums that I'd deleted in Dolphin, which tells me what its purpose is. As the menu item says, it's refreshing the library -- adding any newly ripped albums to Elisa and removing any that have been deleted.
On the other hand, if I leave that setting turned ON, and reboot while Elisa is running in the system tray, when it is once again running in its window, its album list is empty. The refresh operation needs to import all the tracks to Elisa.
Turning that feature OFF is not a big issue. I have no reason to ever leave Elisa running in the system tray, especially if doing that causes such a problem.