For the record, Constellation owners are quite welcome here, heck you are a member of the same Chris-Craft family tree as the rest of us.
The photos of the cap you posted make me shudder. That is a signal of a lot of poor running. I dare say, it looks only too familiar to me and that is sad, because there is a better way.
There are two issues that I can share now having gone through years of trouble, and I know there are many more tips some of the other guys can give too, many of which are in this particular richly informative thread.
The old style crab caps are prone to getting a bit of condensation inside.
This makes any microscopic dust particles stick to the underside of the cap when it dries, and then when moisture comes back I think it just helps create a crossfire. Therefore, my friend, by all means start checking the underside of the cap for moisture. There has been some notion about drilling a hole to vent the moisture (and ozone) that can build up, and I have never tried this (and it may well create an unsafe condition in the bilge if you deactivate the vapor-rated cap). The new aps I am running, by the way, are well ventilated by virtue of a built-in flame arrestor.
The old style crab caps are also not happy with increased voltage (or so I think). This is a hunch that goes back to some older conversations I've had, and drawing a conclusion that more and more voltage may be too much of a good thing. The jury is out on this one, but that is my hunch.
I do know Pertronix recommended KEEPING the ballast resistor intact on the conversion I did years ago, so if you have removed yours then those burn marks you are showing us may well be because you are running way too much through the cap.
In the end out of frustration and less info than I have offered you here, I purchased a pair of HEI style distributors and have been VERY happy with them ever since. They are expensive, about $350 each, but I just wish I had done it many years ago. My issues were a break-up and machine-gun style popping when I reached about 2900 or 3000 rpm, and I just could not tune it out. I never thought about checking the cap for moisture, but it could have been that. In any case, the new units cured that so it was something in the system, maybe the grounding, that was causing me to lose hair at the time. Had I purchased the new units sooner I might still have hair today, but having gone through the experience I do know hair is highly over-rated.
good luck with your boat, let us help you any way we can.