I did some searching; you do have a tough one, there. I can't read Italian, so I didn't learn much. The most promising thing I found was DeNardis Engines, a USA manufacturer of Morini Franco design engines, but it appears to be the same company as Morini Franco USA, and you've "been there, done that". DeNardis Engines has an S6 replacement engine, but it has no transmission, just a centrifugal clutch, and it doesn't look anywhere near as good as your engine; no radial fin head and, obviously, no transmission case. If these bikes were sold in the USA, they probably weren't popular, as you've mentioned. It's more of a mini motorcycle than typical minibike, much more elaborate, so I imagine it was relatively expensive. Also, Italian motorcycles had a rather bad reputation, back then. If someone wanted one despite those factors, they probably were quite difficult to locate.
As is, you have a non-operational bike that's very cool. There are people who have collections of vehicles they never drive/ride.
At the risk of getting flamed: You could replace the engine with something readily available. Obviously, you would want to avoid modifying the frame; tricky, but possible. The 125cc Lifan engine w/ 4-speed manual trans seems to be a popular replacement engine and they are inexpensive. The horizontal cylinder is not ideal and probably wouldn't work with the bike's downtubes. However, the downtubes are bolt-on and could be removed, stored, and replaced by fabricated ones. Adapter plates could probably be fabricated to mount the engine to avoid modifying the bike's frame. Then, there is the 200cc Lifan 5-speed, which would look more appropriate with it's vertical (inclined forward) cylinder, and it should work with the original downtubes, but it may be too tall for the frame. Both engines are 4-strokes, so no 2-stroke cool factor. There used to be lots of air cooled 2-stroke motocross bikes; I remember seeing some with radial finned heads. That could be a good way to go, the right sound, close to proper appearance, and parts availability of a Honda, Yamaha, Kawasaki or Suzuki. As I said, an engine swap without modifying the frame wouldn't be easy, but I've seen it done with fabricated adapter plates. Cutting off the original mounts and fabricating/welding new mounts would be easier, but I would be reluctant to do that to such a fine rare bike.
Hey, if nothing else, give it a detail cleaning/polishing and park it in the living room! It's that cool, IMO.
