Thanks for playing our game and for the feedback.
I thought through your suggestion about adding time based on the health left at the end of the run. I think it wouldn't work well. If the time "penalty" would exceed the time you could lose by bumping into walls, then you would be left with only trying to miss the boost pads with no means of decelerating. If the "penalty" would be too small, your best option would be to lose all the health, so it wouldn't change anything.
As for the optimal strategy, I'm not really sure it is obvious. Would it be going through the whole track with missing all the boost pads and then losing all your health on the wall right before the finish line? Or maybe performing precisely timed wall bumps throughout all the track would work better?
On the other hand, if the first strategy is indeed the optimal one, your idea with time "penalty" for health could work. I could also modify the acceleration curve to make the second strategy more optimal. It could be fun if achieving the worst time would require really precise maneuvering.