So, with what I started this thread for resolved (for now), I have a new problem. I've mentioned it other places in passing, let me lay things out clearly here.
Yesterday I went for a ride, and lost spark. I got it home and started testing things. I pulled the plug and rolled it with the plug on a head bolt. No spark, and the engine whut-whut's steadily rolling it. Finger in the plug hole, and it has compression.
By running the other bike with the CDI from mine, I've pretty much eliminated the CDI, it worked (by the way, the wire and boot were replaced with NAPA parts months ago). I checked continuity on the wiring. On mine, blue checked out from tip to end, and past soldering point. Same for white and black. I get a circuit between the end of the black and pretty much everything else inside the housing, except the ends of blue and white. I did the same check on the second bike (that runs). The results were the same, except that the white wire also makes a circuit with everything else, same as the black, and from the end of the black to the white as well.
Note, a while back I had to switch from black/black to white/black to my CDI as it stopped running then.
So, today I went back to it. I replaced the magneto and the spark plug. There are a couple of marks on the white and blue wires of the old one where they were tight against the edge of the hole they go out of. I checked and each mark was a tiny break in the insulation on the wiring, even if it didn't look like it, so both may have been shorting against the housing. Wired up blue/blue and black/black, no killswitch with the replacement. Tried it a few times and it turns over, but nothing. I swapped to white/black and tried it a few more times and once it caught. The choke was open (lever down) and the throttle was half to full. I normally have to start with the choke closed first thing and can change it after a short wait. So anyway it ran when I kept it cranked open, and stalled out when I relaxed the throttle. It didn't want to restart right after that (and hasn't been tried since, the weather's gotten a lot worse in the last hour so I may not try again tonight).
Just to be sure, I pulled the carb and went over it. Drained it, pulled it apart. The float is fine, the lever seems fine, stem and needle are good. The barrel lifts when the throttle's twisted. Put it back together (less the drain screw) and it dribbles fuel freely at the drainout with the valves open. (Between that and the wet plug I know fuel's getting through.) Cleaned out the 'air filter'/foam while it was apart, it looked a little wet and gritty. The needle setting hasn't changed, and the ilde adjust screw is still snug where it normally sits.
So I'm back to no spark, and just about out of ideas. I'm back to work Monday, so I'd like to get it sorted out before then if I can. There must be something I've missed or overlooked. Fortunately I haven't sealed everything up yet so I can pull the cover and start again if I have to.