Piston engine power at altitude

[ShyTorque]

I don't have access to your data, but the answer is already in your post.

Efficiency = Useful energy got out / energy put in.
Or, in this case, Efficiency = Power achieved / fuel put in.

Yes, the efficiency of the piston engine does increase with altitude, due to lower pumping losses. With a reduction in ambient atmospheric pressure, the piston has less work to do to on the exhaust stroke to clear the combustion chamber of spent gases. More combustion energy goes into turning the prop, (which is where you would measure "power") rather than moving the piston against atmospheric pressure. To think of it slightly differently, the exhaust gas is more "willing" to leave the cylinder, allowing the engine to achieve the same power/rpm at a lower throttle setting, which equates to a lower fuel flow.

Of course the ACTUAL power output may be less, as you realise, due to the reduced charge density, either as soon as a normally aspirated engine starts to climb, or in a supercharged engine, once it has reached full throttle altitude and then starts to climb.

The mixture must be "leaned off" as required to take full advantage of higher altitude effects (actually it's more correct to say "kept at the same a/f ratio").

The other gain in "efficiency" is the IAS / TAS relationship benefits of higher altitiude, albeit not directly relevant to your question as that is really an airframe consideration.

A likely reason your manual doesn't give any data on reducing fuel flow at altitude is just because the sea level data errs on the safe side and the manufacturer didn't actually bother to produce any more data. More flight testing = more time and expense for the manufacturer.