Yes,the handmade/machine made thing is a differant animal from traditional marble making.
I would think,machine made useing your method.If you did it by hand on the end of a rod,with some dopping wax,diamond bronze wheel,finishing with silicone carbide,all by hand on the stick,I would say handmade then.
The one I make,Ill sign with my initial,"G",and then the initial of the company,with the year it was made.
Just trying to give you some ideas,,,,,,
Griff