Interesting question. I read somewhere that prop efficiency was best at about 1800 RPM and as mentioned here the one blade prop is the most efficient. On the other hand there are modern turbine engines that are mostly pushing air that bypasses the jet engine. The turbines have multiple vanes turning at ~30,000 RPM. The vanes could be considered multiple blade props. So there is probably room somewhere between slow moving single blade props and very fast multi blade props that would be efficient at the peak hp range of a piston engine.

There is the heat problem of running any engine at higher RPM's. My O320 run cooler at 2300 RPM as opposed to 2700 RPM. I needed a nice cool day to open it up and keep the CHT within reason. I'm pretty sure that if you put your automobile in a lower gear and got the RPM up to 4000 or 5000 RPM at highway speeds you'll probably have a heat problem.

And there is that cowling problem behind the prop on most planes, except maybe the VariEze and derivatives. Maybe a smaller prop would be more efficient beside or behind the fuselage rather than in front of it. Just thinking out loud here.

Having said all that, if they put the amount of engineering that goes into an automobile engines into airplane engines, we'd probably have better solutions. Rotax comes to mind. Nearly 90% of LSA's use the Rotax engine. Maybe there is a reason for that. Same hp at twice the RPM and half the weight.

One final thought. The PT6 turboprop uses a unique solution of running the exhaust gases of the engine through a separate turbine that runs the prop at a much slower speed. Maybe what is needed is a torque converter to separate the prop from the engine.

Any solution needs to be done quickly before fossil fuel powered engines become obsolete.