> you are bound by the Carnot efficiency, which is at most 35% no matter what(in reality more like 20% or so)

Internal-combustion engines are not limited by the Carnot efficiency; see page 4 of these slides. In fact, latest-generation Priuses gets almost 40% thermal efficiency on the gasoline engine, and large diesel engines -- thanks to lean combustion (favorable ratio of specific heats for the gases that push on the piston), no throttling losses, higher compression ratio -- do even better.

https://www.energy.gov/sites/prod/files/2014/03/f8/deer11_ed...