Why are my distributor cap terminals burnt?

The more difficult spings to compare are the blue and silver.
Before you do anything else, it will be worthwhile to check timing to determine the rpm it begins advancing.

If this chart is correct.
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Then timing between 750 rpm and 3400 rpm will be radically different than my earlier guestimate.
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Need to find out what's really happening there.
If you can find what rpm it begins to advance from 14 to 15 or 16 degrees, great.
Then get at least two more timing measurements further into the advance.
or measure every few hundred rpm, like 750, 1000, 1250, 1500, 2000. Whatever you are comfortable with doing.