I'm having a bit of trouble believing that "the inertia of the two steel flywheels on the splitter is doing all of the work."
Maybe I'm misunderstanding but doesn't the engine remain attached to the flywheel while the ram is moving through its stroke? If that's true, then the engine can deliver power to the ram throughout the stroke.
If you spin the flywheels up to the approximate speed of the engine, say with an electric drill, and then detach the drill, will the device still split a chunk of broom handle?