Ok, I don't want to be taken seriously here I'm a Junior in HS right now, but here I go.
Your first problem as of late is that you plan on vaporizing the fuel in a vacuum environment, ie the head. When the mixture enters the cylinder the pressure of the compression stroke will still recondense the fuel. You have to find a temperature in which the vaporized gasoline enters the the cylinder and the heat of compression sustains the vapor state. One more thing is that vaporization is just and intense form of atomizing; seperating the fuel into molecules instead of droplets. (Yes temperature increases with an increase in pressure, if everything else remains constant.) PV=nRT
When I started reading this thread it seemed to me that, from my chemistry knowledge, a chemical reaction has an equal amount of reactants and products. If you run lean all the gasoline is being burned and there is leftover O2, if you run rich you have leftover. 15:1 is an average for the difference in lengths of the hydrocarbon chains. So my first plan was to seperate the Hydrocarbons to a more controlable mixture, and then crack what is left over. Of coarse that gets dangerous.
My third Idea would take some serious fabrication, more than anyone would want to attemp, but here it goes. The most heat is lost in the combustion stroke of the engine so use the fuel to cool the cylinder. Maybe with a cylinder sleeve/gasket sort of thing. That will definately generate atleast your 475 degrees F. The way you conrtol the temperature of the fuel is with an electric pump, you can speed or slow the flow of the fuel. Like a constant flow water heater. Then you have a problem with excess or too little fuel. You may have to recirculate the fuel. Take carful consideration when you choose the size and number of coils running around the fuel chamber.
I don't think I can do that calculation yet, that will be next year after Calc and Chem AP.
Well some food for thought. Back to my trig homework.