Actually now it sounds a little like your stator. This is Classic Stator failure behavior. Runs great til its hot then dies and is really hard to start and later won't start at all. You may want to test it. As for adjusting the Rear carb low adjuster, i always had to pull them unfortunately. Sluggish on the low end, Does your gas tank hold Pressure?
I was thinking the stator also after lots of research. Thinking about sending it off to be rebuilt. May even send the ebox too.