I confess, one level proves completely insurmountable for me (the Phlegeton crossing). So I decided to resort to cheats, and found them a-plenty, but, alas, the activation procedure is tailored to the Steam version of the game (it requires me to go to the "Launch options" menu in the Steam platform). Is there a way to activate cheats in the GOG version?

Yes it's possible, a possible way to do this is create a shortcut to the game executable on the desktop, then check the shortcut properties, in the Shortcut tab, in the "Target" field, add the parameters accordingly, you should have something like this :
"C:\Program Files (x86)\Apotheon\Apotheon.exe"

Add -dev at the end, so that it looks like this :
"C:\Program Files (x86)\Apotheon\Apotheon.exe" -dev

Note there must be a space before "-dev".