I bet a combined opposed piston engine (ref the Junkers Jumo) modified to six strokes (the 5th is compression and then water injection at TDC and the 6th is a steam power stroke) would beat this wave turbine engine in every respect.
20yrs or so ago, a motor-head friend I knew added water injection to his car.
He swore it increased his mpg dramatically. I saw it. It was real. And these guys were auto mechanics, so they knew engines.