Problem Found!
Added 2017-08-28 09:19:55 +0000 UTCI will be posting a fix momentarily for all the Firefox users :)
So I spent the last while examining things to try and figure out what was going wrong with AW and Firefox. I double-checked all the possible compatibility issues, but didn't find any. I was stumped, so tried a few experiments. Fortunately, this led to me figuring out what was going on.
As it turns out, my code is A-OK, but the way firefox handles loading twine as a whole. The problem was being caused because:
1) The theme--and all the other--settings for AW are set up to be remembered by your browser so that you don't have to change the settings every time you open the game.
2) In the case of theme settings, this means applying the correct CSS style settings so that when you load the game, it's already in your preferred theme.
3) Firefox executes this initialization process before the entire document has been loaded, causing it to try and change things that haven't been initialized (don't exist) yet.
#3 is where the problem is, and kills the game. Unfortunately this initialization is controlled by Twine. Fortunately, there's a simple workaround to restore functionality by not initializing the theme immediately. It's not as pretty, but it will work. :)