First up: Engine efficiency. Since you're still open to changing the engine design: Have you looked at the radial cam engine? This uses a cam instead of a crankshaft. That allows the piston motion to follow any time function desired, rather than the small family of near-sinusoidal motion functions you get from a crank.
If you look at the pressure-volume graph of an idealized heat engine you see a loop composed of four discontinuous curves: Adiabatic compression, additional of heat at maximum compression, adiabatic expansion, and removal of heat at maximum expansion. The area of the curve represents the energy converted to mechanical power on a cycle. An internal combustion engine does the "removal of heat" step by swapping old gas for new, so it usually does it well. But the adding heat step is more problematic.
A normal crankshaft-type engine ignites the mixture shortly before TDC, after which it burns for the rest of the compression stroke, most of the power stroke, and there's still a little left unburned when the exhaust valve/port opens. Some of the added heat comes in too soon, fighting you, much of it comes in late and you only get part of the benefit, and some is just lost. Mapping this back to the P/V curve rounds the corners and drops the expansion curve, showing you a lot of area corresponding to lost energy.
But with a cam-based drive for the piston you can STOP it at TDC and burn ALL the fuel at maximum pressure and density, corresponding to the ideas curve. You can also chose the time/motion functions of your compression and expansion curves so the combined torque of the set of pistons is essentially constant, producing a very smooth motor. And you can run two cycles per revolution, allowing you to run opposed pistons in unison. This totally eliminate unbalanced moving mass and the resulting vibration, while getting the equivalent of a 2:1 gear reduction for free.
Here's some web links to videos of, and more info on, an 8-cylinder "DunVille rad-cam" radial engine for ultralights using this technology:
http://www.youtube.com/watch?v=qvwdQA26fcc http://www.youtube.com/watch?v=OFYlx-rxWgM http://www.dunville.vze.com/. (Ignore the stuff with the bouncing ball analogy.) Note that the 8 cylinder design gets 32 power strokes per revolution. So you can get away with TINY pistons - and as a result a tiny engine - for your application. Note also the extremely low exhaust temperature - which corresponds to most of the energy being turned into work. B-)
Re: Rotating valves vs. poppet valves. The advantage of poppet valves is that the pressure during the compression and power stroke helps seal the valve. Yes it takes a lot of power to open poppet valves. But most of that is stored in the spring and comes back when you let them close. With rotating valves you're dependent on seals that are being pressurized from the sides, and seal technology has been a major issue. Also: The port closing is trying to cut the seal surface up unless you ramp the edge.
Re: Fuel/water/soap mix. Water injection has been shown to improve the efficiency of an (ordinary) otto cycle engine considerably. The boiling of the water does a better job of coupling the heat to the piston than letting the burn continue during expansion, while the water helps prevent loss of heat energy to forming nitrogen oxides. This soap hack sounds like a simpler variant of one that was played with a few decades back: A jet produced a coaxial stream of water surrounded by gasoline. And the jet was vibrated ultrasonically, resulting in a mist of tiny particles with water on the inside and gas on the outside. The gas evaporated nicely, formed an easily ignited vapor, and burned (near the droplets) as if the mix were rich. Then the energy from the burning coating of gasoline caused the water droplet to explode into steam - blasting the remaining fuel through the air and making the rest of the combustion quick and nearly complete, while the water vapor suppressed much of the NOx production.
This, and other, water injection schemes didn't make it into production cars because it would have required TWO consumable liquids to run the engine. The auto execs didn't want to put this double-fueling load, and problems if one liquid ran out, on the car owners. I'm not sure whether water injection is applicable to your contest, but I suspect the issue is moot.
