-it is not possible to generate the energy necessary without burning the fuel to do so
But it is possible to generate the energy without ****ing unburned fuel out the exhaust and, thus, generate the same energy with less fuel.
But, instead of sitting around vegetating, lettuce take a quick tour of the thermo-chemistry.
Let's start with the red knob at full rich. You are dumping too much fuel in the cylinders to do anything except keep things cool. Trying to eyeball the picture in the Lycoming document, it looks like you are putting more than 20% excess fuel into the cylinders for the air flow. This excess fuel goes right out the exhaust as unburned hydrocarbon and CO. At 17 gallons an hour, $6.00 per gallon, that is more than $20 per hour out the tailpipe unburned.
Pull the red knob back to best power. About 150 ROP per the Lycoming picture. You are still putting excess fuel into the air, but since hydrogen burns easier and burns hotter than carbon you generate more power than you would at the chemically correct fuel / air mixture. Figure about 10% excess fuel - but because of the preferential burning of the H it only costs about 5% in brake specific fuel consumption (pounds fuel per horsepower hour) compared to the chemically correct mixture.
Lean to stoichiometry (chemically correct). This happens pretty close to peak. Now you are have the correct mixture of air and fuel to allow purd near all of the fuel to burn (some is quenched at the walls and in the crevices). Because you are not preferentially burning Hydrogen, you are down a few percent in power if you are at the same manifold pressure that you used for best power. Depending on altitude, you may be able to make up for the loss of power by opening the throttle and getting the same power/ speed along with a nice reduction in fuel consumption. Or, without opening the throttle you get the same power as running full rich (again per the Lycoming picture) but with an even bigger reduction in brake specific fuel consumption (BSFC). Your car runs right at stoichiometry 99+% of the time to make the catalyst work efficiently.
Lean to best BSFC. About 50 or so LOP (per Lycoming diagram). Here you actually have some excess air in the cylinders. The improvement in fuel consumption (as the same power) is modest compared to peak - about 2 or so percent. This comes from two sources - opening the throttle more to maintain the same delivered power will reduce pumping losses. And, there is some reduction in the heat lost to the cylinder walls. If you don't (or can't) open the throttle to maintain power you do lose power (about 7% compared to best power). As a result, if you lean at a constant manifold pressure / rpm your reduction in fuel flow looks better than the actual improvement in BSFC. Running here reduces the stress on exhaust valves a bit and would generally be more popular than running at peak (except in your car as previously noted) even though the improvement in fuel consumption compared to peak is small.
Lean to rough. At this point, you start to get slow burns and possibly even misfires. BSFC starts to go back up because the flame speed has gone down and you aren't burning the fuel efficiently (it burns too late in the cycle to get all the work out of the fuel energy) - slow burn and misfire cycles are even worse. Not much point to running at this mixture. You could re-design the engine to push this point out further, but the gain in fuel consumption at constant power will be modest and, unless you are turbocharged or at a lower altitude, it will not be possible to maintain the desired power levels.
