Ah, the dilemma of the innovator: is no one doing this cool thing you've thought up because you're smarter than everyone else? Or do you mistakenly think that you can make it work because you're an over ambitious dolt, about to chuck a whole bunch of man-hours down a rat hole?
While I had my tongue in my cheek about the response that one may expect at the idea, I was quite serious about the potential for the system to work: a Hubin timer, a helicopter engine governor, a servo and a small battery (and an RC carb), and you're all set. You'll probably add at least an ounce for all the pieces. On the bright side you'd also get a dead-steady run (or at least as good as the governor will get you), meaning that you wouldn't need a super-special razzle-dazzle black-magic stunt-tuned carbon-fiber-piped engine -- just go to the local hobby shop and pick out anything that is reliable and that'll haul your plane around at 1/2 or 3/4 throttle in the level laps. You'll have power to spare for when you go straight up, and "shut down" to spare going down.
Or if you just want the timing capability without the governing, you can save a part and some weight and do it with a Hubin timer, a servo, and a battery. If you can figure out a reliable way to cut the power under servo control without a carb, you can use your favorite ol' reliable CL stunt engine.
Ways that I know that the free-flight guys use to cut power are a pinch-off timer, where the timer actuates and pinches the fuel line, making the engine run out of fuel, and a flood-off timer, where the timer actuates and un-pinches a fuel line that is directed into the venturi. Obviously a flood-off timer requires a pressurized fuel system, but I think that muffler pressure would be more than enough.
In either case you'd really want to talk Will into modifying his timer software to start up at the full power setting, stay that way when the button is pressed, and only go to low power at the end of the flight. You could work around that, but it'd be awfully nice.
After that, the rest is just mechanical ingenuity.