OK, lots of time in the garage this weekend.
Ground wires from battery and engine to frame all seem to be fine. There is maybe a bit of "gunk" on the engine one, but I wouldn't call it corroded by any means.
As I mentioned, I put in a new spark plug. I did not clip the coil, since I have a second coil around that I tried. I figured it would be unlikely for two to fail.
Wires from the stator. This was a new level of tinkering for me. I took off the fan thing, the inner hub cover. Wires looked fine in there, although I didn't get all the way to the stator coils. I followed the set of wires up from the stator back to the rear of the scooter. The wires looked fine there. There was one bullet connector that felt looser than it should be. (blue/black I think.) I pinched it tighter but it didn't help. And when I unplugged it completely, no startup actions at all. My problem is a I get the starter motor cranking, but no spark.
I did actually go in and disconnect the handlebar kill switch. It was by no means a fun task to dive that deep under the plastic, but I think I did it without breaking anything. Unfortunately, it didn't help. Still no spark.
Perhaps some background would help. When the problem first happened, it was very cold outside, and since I'd ridden the bike that day and parked outside, it got hammered pretty good by wind and bitter cold. There was some battery juice there, though, but it was pretty weak. (I've since replaced battery.) I tried kick-starting, but the rod broke off! So I had to have my brother-in-law come pick me up with his truck. Anyhow, that was the last day it started. There had been some oil coming through the air filter box (probably an overfilled crankcase), but other than that, it had been working great. There was maybe a bit of "hesitation" at high speeds, going down hills, where it felt like the throttle would "slip" a bit or something. But it never was a problem other times.
Any other suggestions would certainly be appreciated!
Vance