Just an update - about 30 days later and still running strong. I hope I don't jinx it...

 

The no start condition returned again, most likely due to the cold weather. After a little bit more electrical testing, I finally was able to pinpoint the problem. It was a bad ground. I am confident of this because I am now able to repeatedly reproduce and overcome the problem.

It appears that the original grounding point even after cleaning, etc. was not providing sufficient conductivity. So there wasn't enough current whenever trying to re-start in the cold, rain or even just after a few minutes of running and trying a re-start. The battery likely wasn't re-charging quickly enough or completely (which is probably why the alternator gauge readings looked a little high during the no-start), and there wasn't enough current getting through to ignite the spark plugs until the battery "rested" for a while.

After I attached the negative terminal of the battery to a new grounding point with good conductivity, the problems went away. It even worked when I experimented with the battery about 25% to 35% discharged.

Hopefully, this will help someone!