Anyone try two engines on one bike?

I have a Raleigh women's cruiser bike on steroids that I call "Girlie". She's had a 72-volt electric motor but now runs a Mitsubishi 2.2hp engine with tuned pipe, friction drive and 1.5" roller. I had a 1.125" spindle on it, but the engine redlined at 20-something mph. Acceleration was good, but the engine overrevved if I tried to keep up with traffic. I wanted more speed, so I installed a larger-diameter spindle.

Since I installed the bigger roller, I can live with the soft low end because I now ride safely with the flow of traffic. I also like the top end, but I need more acceleration. Also, hillclimbing needs improvement because of the 1.5" spindle. I COULD reduce to a 1.375" roller, but the thought of running engines front and rear fascinates me!

Here's my idea: One solution would be to install a second engine, like a Staton front-mounted friction kit designed for trikes. To simplify matters, I'd use another 2.2hp Mitsubishi engine and a 1.125" roller. This would give enough low and midrange power to scream to 25mph. At that speed, I release its throttle back to idle and floor the rear engine, which had been idling all along. With the 1.5" spindle, the rear engine takes over for high end duties while the front engine idles. If the engines are identical, it'd almost be like shifting gears.

Do you think it'd work?