Cheap can take many forms, I have a few of them.
What can start off cheap as an initial but can end up costing a lot more over the course of the project.
I would think a cheap $500 street bike would be where I would start then you don't have to worry about titles or street legal etc.
Adapting a final drive from a shaft bike I think could easily dwarf the initial higher cost of the actual bike.
I hear you on using what you have, and the cheapness, but also factor in that somecrazy adaptation is going to require machine work and that ain't cheap.
Maybe if you give us some more details of your abilities with fabricating and what your limitations are as far as riding, it would help get some better advice.
I think a scooter would be a great option and they are really cheap it seems
We're not out here to rough it. We're here to smooth it . Things are rough enough in town.