Why are my distributor cap terminals burnt?

the coil you have should work fine.
my opinion is something is making the ignition work harder than it should. Have you eliminated the ballast resistor? if the coil is a 12 volt rated coil you don’t need it. Also check voltage at the coil + terminal with the key on. And are all your engine grounds good as in low resistance from block to heads.
Oh I about forgot also make sure the spring contact on your rotor button is making contact with the center electrode on the cap.