I hope this doesn't show as a duplicate message, I thought I had responded, but no message has appeared...
Before you condemn the internal gearing of the furler gearbox, be sure that the drive pin is engaging in the drive plate. A number of people have reported having the hole enlarge and roundoff, which drives the pin out of engagement. That matches the symptoms you are seeing. We have had that drive plate fracture and totally fail.
I have just had our jib furler gearbox completely disassembled for normal maintenance of seals and bearings. It seems very unlikely that the gearing would cause the issues you describe. Mind you "unlikely" is not impossible!
We have twice had to use our manual furling system, and never had any trouble with it. Our furling line is standard 10mm double braid polyester line. I wonder if the StaySet is just a little too stiff? I am sure that 7/16" line would not be too large for the drum.
Locally, the go-to guys for Amel rigging are Nance and Underwood in Fort Lauderdale. If you needed a new drive plate made, they can do it for sure. Roger Underwood is the guy to get in touch with.
Fort Lauderdale, FL, USA
Back underway tomorrow morning! Finally!