If its not surging, I'm leaning toward weak ignition as well. You can try filing the points (I know you are supposed to 'replace' them, but I'm old school.) Try a 'known-good condenser and make sure its body has a good ground.
Another think I am seeing occasionally on these engines- The 40+ year old insulation on the wire from the coil to the points deteriorates and actually arcs to the clips it runs through at certain times, especially when the ignition load is anything more than minimal.
Its always the condenser.
Ok, OK, its not always, but its quite often the remedy and its cheapo and easy to change so it has become my go-to whenever I have one that seems mechanically sound but does not start or run quite right.