I have one at home. I can't remember offhand what actually winds the reel mech. on a Bally, but I'll try and get a look when I get in.
You say the mech. operates outside of the cabinet? Well, that sounds promising. It's just a 'missing link' somewhere.
My first thought was that you weren't getting the mech. into the cabinet properly, but on a Bally, that's virtually impossible.
I should know more by tomorrow.