I am reasonably sure I'm giving up on reviving the CM200. I've been PB-blasting the motor for weeks and I still can't budge it. Luckily, I haven't invested into it very much. $100 for the bike, $40 for the clutch and that's about it.
Meantime, I ran into a 81 Yamaha Seca 750 on CL. I think I might have overpaid, given that it needs a carb overhaul, but it runs and drives. You just gotta fiddle with the choke to keep it idling.
So far I fixed the ignition lock and bought a few electrical parts. The glass tube fuse holders are, apparently, notorious for falling apart on these.
The bike came with an extra set of carbs. Which means I can mess with them without disabling it completely. Now, I'm going to see what I can get for the Honda...