While you say that your points "look like I would expect points to look", they will not remain that way for very long without a ballast resistor.
Its hard to tell you from here, what is causing your poor running issues, but is easy for me to steer you in the right direction to keep you from having another reason for your engine to have a poor running issue in the near future.
As you have alluded to, it is best to do your diagnoses at the exact time the poor running issue takes place.
When it acts up again, be prepared to immediately do a spark test at a spark plug, and/or goose the throttle while looking down the throat of the carburetor to see if there is a squirt of gas entering from the accelerator pump (this will let you know that there is fuel in the bowl of the carburetor).
