Just a couple of thoughts.
1) I think this problem is carby related. I have fixed up a number of these edger�s and the newer ones usually only have carby issues.
You never mentioned blowing the carby clean with compressed air. I would recommend if you haven�t. I have found issues in the past with genuine and aftermarket needles being used with genuine and after market primer caps. The black needles (aftermarket usually) are usually shorter and I hardly ever have a problem with them however the bright coloured needles are longer (usually) and if you don�t use them with a genuine primer cap you will have loads of trouble with erratic running. So� make sure you match genuine with genuine or aftermarket with aftermarket. Some don�t like the aftermarket stuff but as long as you match the stuff up correctly it should be ok.
2) Minor hole in the float (check for liquid in the float)
3) A new primer cap might be required (clean it out with compressed air first)
4) Clean jet with compressed air.
5) maybe the exhaust is blocked so try another one.
Keep at it.
Jaffa