Is there a method to drifting that doesn't involve flying off the stage?

Dont boost while you're drifting

I first did that stage without even drifting. You only need to lower your speed and it's possible to finish this level in under 1:15 and getting all the medals. However, the only way to get a S rank is to be quick so you need to drift.

For a good drift, start from the outside of the turn and a little before you reach the starting line. If you don't know what I'm talking about, there's an horizontal line on the floor right before a turn in this stage.