I would like to see a feasible left side shifter too!
Heck, I'm all about gears.
I can see this working with a thin enough back wheel and the sprocket cupped way in to compensate.
The thing is, no matter how you look at it, single speed chain needs a straight line of travel, heck even 10mm or a small sprocket wobble will cause a chain jump.
Maybe if you used good 7-speed chain, sprockets, and some sort of derailleur type sprocket guide on the bottom return path to 'bend' the chain to hit the sprocket teeth it could work?
I wish the best of luck and success with this bud, I truly do, just keep the dynamics in mind is my last apparently unwanted advice.
*bows out*