Another approach could be to use a large sprocket, and one stage of the FP gearbox. We did something similar last year.
this is the gearbox we made, using two sheets of aluminum, some hex shaft, two bearings, and one gear from the FP gearbox. The second plate is not shown, nor is the plywood spacer.
here is the gearbox driving a larger sprocket with a chain.
I don't know if this idea will help you, but it could be easier to find a premade pair of sprockets, than to get a gear machined?