I've recently decided to take the TARDIS mod by drekmoor, and edit it to play music from Doctor Who (stuff I've bought on iTunes), only to find that there are only three possible music types (Default, Public, and Dungeon). Is there a way to add another music type, which works in the same way?

No, but you can use the http://cs.elderscrolls.com/constwiki/index.php/StreamMusic command so that your tunes play inside the TARDIS.