Just another $0.03 cents worth....
First off, I am not sure what that swill is that there selling at the pumps is, but it is not real gas. Anything that burns and can be tested to have a specific octane rating can be sold as pump gas. Higher octane fuels have a better chance of being a better gas to start with, I think that is half the reason more premium blends work better, and not the octane needs?
100LL (100 octane Low Lead) makes it's power and resist preignition by being a very pure form of gas. Pure un-blended gas just burns evenly. Burning evenly and not raising pressures and spontaneously combustion , (preignighting or for the lack of a better word, partly explodes).
Pump gas with additives to control the octane are 'less then' real gas.
I will admit that I am far from understanding what octane modifiers have to do with an engine that is pumping above 10K RPM's and never sees full volumetric efficiencies? But I can see some getting a boost with a more aggressive burning fuel (pump gas).
A couple things Av-gas needs is a low RVP (ried-vapor pressure) to be used at high altitudes, that might be a little harder to get a good eggressive burn at slow speeds (strong idle). And harder to start with a cold engine?
Av-gas is designed for long-stroke 4-cycle engines, it might be a little slow in faster turning engines? (but a real gas is hard to find anymore.
If an engine looses power with Av-gas, I would be hesitant about leaning it to make your heat gains, there is a chance it might come back with just a slightely hotter plug, and could use a slightely more ingition timing to beat the pump fuel in the same engine?
Flame propagation is everything to making power.
Av-gas just plain has more power in it, if you can burn it completely.
A simple test would be to run Av-gas, and again with pump gas with out a muffler, at night, just to piss your neighbors off, and watch for how long the flame cone shoots out the engine?
If there is a lot more cone with 100LL, my bet is that tuning that back to the pump-gas's best, will beat he pump fuel hands down?
Cylinder temp and EGT would be a fun test to use with other ideas, like making the same temp with Av as you got with pump fuel. But a pressure crystal inside the cylinder would be the real instrument.
It is my bet that the pressure comes up a lot slower in a saw that dose not do as well with 100LL ?
A simpler comparison would be summer - winter power gains comparing fuels.