Why are my distributor cap terminals burnt?

Righty, your distributor plate has a series of holes around the outside. They could be there to limit the mechanical advance. If so, set it to ~ 20 degrees. Set initial timing to ~14 degrees.

The outboard carbs could have stuck needle and seat or float [dry bowl syndrome]. And when their throttle plates open up it creates an overly lean condition so that the combustion mixture doesn't fire.