irishpowerjunkie,
You're using the string trimmer's clutch? How long has that system been holding up? Even with a top-dollar trimmer, I can't imagine the clutch driving a bike for very long.
Plush,
I've only done friction drive, myself. One of these days I want to try a weed whacker, chain drive, skinny tire ten-speed. (I have quite a few 1970s Schwinn continentals and varsities & parts)
Their narrow frames are not ideal for chain drives. But I know how I would mount a rear sprocket. The hubs have big ol' flanges; just under 3 inches diameter. Looks like they could be drilled out for bigger gauge spokes. And there are 8 holes already in the flanges. These are the old Made in France "Schwinn Approved" parts.
In the picture you can see a 1/4 x 20 bolt easily passing through one hole. Below it a 5/16 bolt almost goes through - two strokes of a round file away from fitting.
So if you see an old schwinn being tossed, at least grab the hubs. They would be good for making a jackshaft, too. I also used one for the tailstock of a homemade wood lathe.