The Austin-Healey Sprite used in this showcase is a car with a slightly wider gear ratio to torque. Shift down to third gear immediately after the start. With the exception of a few straights in this showcase, we basically use third or fourth gear and rarely use more than fifth gear.
The downside of the Sprite is that it's too light. Puddles of water should be avoided where possible. If you break into a puddle, downshift immediately.
Some corners can be cut short by entering in a straight line. The first corner into the quarry is especially important as it not only allows for shortcuts, but also to avoid puddles of water.
Showcase Remixes are scripted. It does not really matter how good or bad you do. Only last one or two checkpoint matter, I've had opponents wait for me when I lost them before. But when you do really badly, not even the waiting of opponents will help you. Main thing is to keep the gas floored 99% of the time, go shortest path and avoid water and obstacles. I did this one on first try on Pro difficulty every time.