Why are my distributor cap terminals burnt?

it's OK. It's normal especially when at the time it you determined the main issues were mechanical.

So lets see what you have and I'll try to help you make the changes in the right direction.
Do remember what springs were in it?
We can estimate from 45-22=23* that may be the advance limit. That looks about right from the photo. Or if you have the distributor apart, measure it with the keys.
Finally, is the engine hot rodded at all and if so what duration and compression?