Oh! I never noticed Adobe Acrobat ^L mode!
Going to full page mode is not that onerous as you only need to do it once per session.
OTOH, you still have to Alt-Tab to get back to Calibre to select a new piece of music, right?
Windows is kind of a pain. I've just made a new Bluetooth device for switching apps in Android. I can have a dedicated key for each app. This is not like Alt-Tab go to the next or previous app. Although in your case, a simple Alt-Tab would be good to go back from PDF reader to Calibre. But if you hit it twice you've gone back too far.
I've got it easier because guitar transcriptions are simpler and I've got it all integrated in one application. I just hit one of the four foot buttons and it goes to the next piece of music in the list, without even flashing the list.
Edit: I looked at this Adobe PDF stuff. Ctrl-L works fine, but it's not idempotent, i.e. you keep doing that it goes back and forth. I had an old utility that I wrote and it still appears to work just fine, but as I said, it will turn full-screen back to normal too.
Code:
C:\>wndctrl "*Adobe Acrobat*" /kctrl-l