Adam, yes you did look into that.
If you give me FTP access to your demo, i can reproduce it.
All i changed was in case of 404 error, show a 404.html page instead of blank page and the folder URLs started redirecting to 404.html page.
If you want to make that change in your dev site and try it out ?
What i figured is that you have if (!$file) then show 404. This will need to be changed so there is a OR statement that if a user is viewing a folder, dont redirect unless there is no such folder available.
For your 404 on folders, you have the script to redirect to homepage instead of 404 or blank page..