Nice. I think Randall has a great idea -not that he generally doesn't.
Your "test" video is different from the last "test" run because the hood (bonnet) was open the whole time. I think the air intake temperature rising is causing the drop in idle. Your ammeter goes to discharge when the fans come on, which should be expected. I'm not sure where your alternator "cuts in", but raising the idle a little might keep it charging all the time. (I have my idle set to about 1,000 so I never get a discharge.) But I don't think your problem is electrical.
Anytime I run my car in the garage, I put a box fan in front of it to bring in fresh air. I think if you ran your same test again, with the hood closed, your car would shut off sooner. Hot air being sucked into the carbs acts differently than cold air being sucked in. And I assume the temperature of the fuel coming in also has an effect. A closed hood would allow the carbs/air to warm quicker.
I think I'd try running it without the alternator connected, and you might find it does the same thing. -That doesn't prove you don't have a bad coil, or the problem is not electrical, but I think your efforts would be better spent looking at ways to keep the fuel cooler. Do you have a way to measure the temperature near the carbs?
It gets warm here in Texas. One of the things I did was replace that fuel line from the pump to the filter/carbs with a larger line. I had trouble with that goofy sized feral leaking and it was simpler to go with a larger sized pipe/fitting. Also, I see your fuel line goes really close to the front of the block. Mine is farther away. I've heard of people putting wooden clothes pins on the fuel line to act as heat sinks, but that seems a bit silly.
Interesting problem. I'm guessing that if you had a volt meter attached to the input side of the coil, you wouldn't see a significant change until the car stalls.
I know I'm sort of rambling, but I like sharing your problem. If I knew, I'd tell you what was wrong.