As far as I can determine, Schone is actually a private brand that only Alrossa sells. So, they were probably getting those spiral handles from somewhere else to assemble into the razors they offer.Afaik, the only one who still has Schone razors in stock ( or the only one I could find) is Alrossa and like you said they sell them on Amazon. I bought mine from there, but since i'm from Europe I had to send it to a friend of mine and then he send it to me along with other razors and there's no way I can return it or do anything about it. Since I sold my Fatip OC i'm using the handle of my FOCS with the Schone head.
I've tried shaving only once with the Piccolo handle and I think that's the worst handle i've ever used. It's super small and slim and even the ball end handles for Tech and NEW razors are way better. At least the head doesn't have issues and I might ask around the local facebook shaving groups if anyone doesn't like his Grand handle and wants to trade it for mine. It's a long shot, but I have nothing to lose.
There are some other handles that can fit on the Fatip threads. For instance, vintage Gillette 10-32 threaded handles, vintage Star razor handles, etc. You might try something like that. A fat handle from an old Gillette Tech is not bad if you don't mind something short.
I really like the Piccolo handle, BTW. Try holding it like a pencil and/or choking up on it so your fingers are directly under the razor head. Very maneuverable that way.