SAS
So basically IO you are saying that power is a made up figure from torque and engine speed!
YES.
But power is not some artificial concept, no more than "10" is a "made up figure" by multiplying "2" and "5"
Power = torque x RPM
Also, power directly equals thrust. A prop which absorbs X HP (at a reasonable blade AOA) will deliver Y newtons of thrust. I can't recall the multiplier but assuming say 85% prop eff. it is just a number.
Also, fuel flow equals power. Again, a straight formula, X GPH gives you Y HP - assuming stochiometric combustion.
IF you have the option of a gearbox (so no need to compromise the engine design because the prop tips mustn't get anywhere near mach1) and IF you have a VP prop (so the engine can run at a narrow RPM range for both takeoff and cruise) then any old engine delivering X HP will do the same job. Torque doesn't come into it.
The Lycos are designed (compromised, but everything is a compromise) to avoid a gearbox, so they run at a low rpm. Obviously an engine rated at 250hp at 2500rpm needs to deliver double the torque of another 250hp engine that does it at 5000rpm. The problem with the latter is that a 5000rpm prop is a problem (efficiency and extreme noise, and would have to be of a small diameter to remain subsonic).
Turboprops have a gearbox because a turbine cannot possibly be compromised enough to rev low enough.
If an engineer came into this from scratch, he may choose a 5000rpm engine (petrol or diesel) because such an engine is going to be a lot smaller than a 2500rpm engine of the same HP - even though the gearbox will weigh a lot, and won't be reliable unless it is expensively robustly engineered (which isn't going to happen).
Or he might choose to copy a Lyco (avoiding a gearbox) but design it better, with better heat transfer and FADEC. It could be a diesel too, although that doesn't change the basics (except diesels hammer the gearbox more).
If you start with a car engine (Thielert) you won't get any useful power out of it at 2500rpm, so you are stuck with a gearbox.
I am no engine designer but did loads of this at college+univ, and I would bet that the best GA engine would be something big and slow, burning jet fuel, without a gearbox, with electronic ignition+management, and air cooled.
Air cooled, because unless one does spacecraft-quality plumbing (which won't happen) it will leak and if it leaks you have an near-immediate engine failure.
Advanced materials could be used because the budget is huge - a new IO540 for example is about 25 grand. The cost of materials doesn't even feature on the costing.
I am sure this has been discussed here before.