Moving the engine may improve the bike or ruin it.
As stated in other threads here, a lot of engineering goes into the precise placement of an engine in the frame of a bike. A half inch in any axis can result in a great handling bike or a nightmare, especially an engine like the Norton, which has certain harmonic frequencies at different engine speeds.
As an example, I can think of the BSA Rocket 3/Triumph Trident. The BSA used a different crankcase than the Trident, rotating the cylinders somewhere around 10-15 degrees forward. This didn't alter the center of gravity much, but vastly improved the handling characteristics over simply dropping the Trident engine in the BSA frame. Unfortunately, the slightly better-handling BSA did not have as comfortable riding position as the Triumph, and BSA stopped selling motorcycles under their brand right around the time they came out with a 5 speed gearbox for the A75/T150
I noticed a chopper at a local bike night a few weeks ago that had one of those monster rear tires on it - a 360. Instead of offsetting the engine, the final drive had an offset sprocket mounted on the swingarm pivot. Chain went from the transmission to the intermediate drive sprocket, final drive belt went from intermediate driven sprocket to the rear wheel. This way, builder kept his standard engine layout, but could put any width tire on the rear he wanted. I've also seen intermediate sprockets on bikes with hyperextended swingarms - 2 100-link chains rather than one 190-link chain.