I think someone should do this run, it's faster than the other two and there are quite a few shortcuts within the levels. I started one, but If it's for pure speed it's terrible.
I've done up to the Launch Base Zone if you want to look at it, getting all the emeralds by the first ring in Carnival Zone (I've done better at proper speed though) and using Super Sonic throughout. I found a glitch in this level though when I was playing it and didn't want to retry it as it was so annoying the part I was at that I had gone through a lot of the rerecords (The is in the Carnival Night Zone). I'm sure it can easily be beaten and can easily have more interesting things in it, but I was doing it for fun at the time. If I get through it, I might do a retry before September.
You can get this at my new born, but rarely updated
http://www.freewebs.com/gamemoviefiles/. If anyone wants their movie there (not .avi please) just follow the About page. I havn't bothered to make a requests page yet.