Thanks to enterprising GridCartographer user rikkles (@RikRetro on Twitter) you can now natively play Apple II games through GridCartographer, as he added support so that GridCartographer and AppleWin can hook up with each other (similiar to how the developer of GridCartographer created a custom DosBox version to hook up GridCartographer with Dos games in the past).
This fork of AppleWin can be found here (and also on the official GC website now) as well as some profiles (Ultima 4, Ultima 5, Wizardry 1) to go with it. If you're not entirely sure what this means, once users have created game profiles and provided a map, you can either use automapping in games that have never supported it or if you prefer you can draw your own maps while playing (similiar to Etrian Odyssey). Since various profiles and maps for classic dungeon crawlers have already been created for other systems (DOS, NES, SNES, etc.), you can expect the Apple II versions soon to follow (I just used the existing profile for Might and Magic 1 to get the existing map to work with it for example).
This development is really exciting, as the Apple II has a couple of dungeon crawlers that never been ported (Centauri Alliance for example) as well is home to many of the original versions of the most classic crawlers we know today.
As an amusing side note, I've managed to play old Apple II games in GridCartographer in the past by linking it up to DosBox and then loading ApplePC 2.52, an old Dos Apple Emulator, to play the original Wizardry, but since the emulator is quite old there are certain limits to it, first of all it doesn't support the more recent WOZ file format for Apple II disks. So good that we now have native support.