Logitech Craft Keyboard will not re-connect to Macbook Pro after Mojave upgrade

I've got a Logitech Craft multi-device Bluetooth keyboard (along with a Logitech multi-device mouse) that I use for switching between my 2017 MBP and a Windows 10 machine.

Prior to upgrading to Mojave, this setup worked flawlessly, easily switching between the two computers using hotkeys on the keyboard & mouse.

After upgrading to Mojave, however, I've lost the ability for the keyboard to switch back to Mac OS after switching away to Windows. The mouse works fine; it's only the keyboard that's at issue.

The Mac OS Bluetooth manager seems to know the keyboard is still there (it's visible as a connected device), but it doesn't work. To get it to work I have to delete the device from the Bluetooth settings and re-add it.

I've tried lots of things to fix, including: cycling Bluetooth on/off on the Mac, rebooting the Mac, power cycling the Mac, deleting the Bluetooth plist file in Library\Preferences, power cycling the keyboard, etc., etc. I've also upgraded to the latest version of Mojave (10.14.3) and upgraded the so-called Logitech "Options" software which is a configuration app that I'd suspect has the latest drivers. Nothing works.

Without the ability to switch back, the whole setup is useless, and it's ESPECIALLY aggravating because I did not want to upgrade to Mojave in the first place but only did so to get rid of the persistent and obnoxious upgrade prompt that has no "Ignore" or "Cancel" option to just make it go away.

I've also posted to the Logitech Support forums and have seen a few posts about this problem, but no solutions. It seems fairly obviously related to something introduced in Mojave.

Suggestions?