I am submitting this now without a Coyote run to complement it. Apparently being 1.5 seconds faster in the first two levels of the Coyote run throws things off somehow in level 3, and Wile E. is refusing to hit the spinner in such a way that gives him that massive speed boost seen in my first submission. Getting it to cooperate is going to take some time, so I present you with this in the meantime.
It's the pretty much the same thing as the original submission, but nearly four seconds faster. Some of it came from simply handling things better and using the beepbeep more often, but most of my savings came in Train 2 where I stumbled upon two extra turbos that weren't too far out of the way. The end result, even though it's only four seconds, is much more enjoyable to watch this time around.