Hi Matt, managed to grab a save file online that's an exact match of yours (6/13 reverse course and 8/9 movies). Apologies first of all as I wasn't too clear in my above posts.
In Single Race mode, all forward tracks should be selectable. Go to the first track Red Rock Canyon, select laps and you should see Reverse has alreay been unlocked on this track only! Select Reverse here and then get 1st place; you will get a message after the results screen saying another reverse track is available (it will be Newtown Express Way). Then select Newtown Express Way and race on that reverse. Repeat until all remaining 7 reverse courses are unlocked. Make sure you have your VMU to Auto Save:)