The ability to set actual ignition timing far outweighs any advantage of electronic ignition.
If your set up has 12volt battery and charging system, you could fab up a really nice electronic ignition using a chrysler or GM HEI ignition module and coil. A lot of effort, just to eliminate points.
Has anyone tried using a flywheel from a vertical shaft rotary mower? They weigh less. 50 yrs ago I put one on my side popper go kart, was tough to pull start, but would rev up quick, so quick it out powered the centrifugal clutch. Maybe the clutch was worn, I dunno, was just a 13 yr old kid.
The ones that run rich on the main system, possibly the main air bleed or emulsion tube is blocked or restricted. This is where the fuel mixes with air to form an emulsion. Not enough air and it will pull more fuel from the bowl.