Why are my distributor cap terminals burnt?

As far as timing curve goes
Lets see what would make sense for the next trial.

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It there's nothing obviously wrong with the distributor (cap rotor wires pickup)..
First check will be a mechanical measurement of the advance limit. Use the keys or drill bit.

If you want to go step by step, accept that for what it is right now.
Change one of the springs for a black spring, which I beleive is the longest.
It should be a little loose, no tension upon installing. If so, great.

^This will result in just one blue spring holding the advance back at idle.
Therefore timing should begin advancing at a lower rpm.

Optional trial sequence.
If having a 10* limit is just driving you bonkers.
Increase advance limit to what you think will be 20 degrees instead of 10.
That will put a lot more tension on the springs.
That will delay the begining of th advance to a higher rpm. Opposite of what we want.
Therefore
Change one of the springs for a black spring, which I beleive is the longest.
It should be a little loose, no tension upon installing. But it may not be.
Therefore bend the perch just enough inward so the black spring is loose.

Going this route its hard to predict whether this will be enough to get the advance to begin at a lower rpm.
Either way, retest and see what the results are.