So the points were bad. Relatively new (500 miles) but the contact end popped off of one side and you can see the marks from it only having a partial connection to the underlying arm, which would explain the sudden change in running. Doesn't explain the overheat.
The multimeter was also showing some continuity through the distributor terminal insulator: about 30 ohms. Took those little blocks off and can't see any cracks in them.
