I was able to change the SYSTEMMIME file like Pingy suggested by downloading it, editing it with what I'm guessing is a binary-safe editor (PNotepad), and replacing the server file with my local copy. It didn't really seem to do anything, though. I downloaded it again to make sure it retained my changes, and also viewed it through the CPanel manager.
I'm still getting the 500 Internal Server Error.
Another thing that's a little odd: When I added a mime type via CPanel, all it did was directly append the 'AddType' statement to the end of the .htaccess file, which made every file on my site return a 500 Internal Server Error. It screwed up because there wasn't a new line between that and the previous statement, but that might have been my fault. I've fixed it, though.
EDIT: It doesn't look like the SYSTEMMIME has any purpose other than caching the system MIME handlers, kinda like mysql-db-count (I had to test it, I was curious). On line 51 of the file, where the php extensions are defined, I changed "php" to "pht", and my site still shows up normally. I logged into CPanel, when to the MIME page, and showed pht as one of the extensions.