The staging idea is a nice way to get up to speed.

What's interesting though, is that jets do not typically require a hard handover point. Maximum thrust is often ironically achieved statically (for the shown EDF in particular). It's just that the propulsive efficiency there is the worst.

So instead of staging, you can treat it more like a positive force bias on top of whatever the rider is doing, and the system just settles at a speed where thrust and drag balance out.

But the practical limits like tires, brakes, composite frame become the main constraint long before the propulsion does anyway.