Small Engines (Lawn Mowers, etc.): Honda G400 engine misfires, honda generator, head temp

Question
I have an older Honda G400 powered Honda generator.  The engine starts okay but needs several tries to keep running.  Once warm, it runs well but has a noticable misfire every few seconds. I can see the misfire puff some air through the carb and also hear it in the exhaust. As a generator, this engine is elec start, has a head temp sensor, low oil sensor, electronic ignition (I think) and an auto (and manual) choke.  I took the head off today thinking my problem might carbon build up in the valve seats.  Nope.  In fact, for an older engine, the carbon was minor and the intake and exhaust valves look good.  While in there, I did clean the carbon and lightly grind the valve seats (just to remove the minor carbon).  I also removed the carb, disassembled, cleaned everything, and reinstalled. When reassembled, the G400 ran maybe a little better but still misfires.
I would like your thoughts on what to try next. I am thinking the timing may be off but I have no idea how to address that if in fact this engine does not have points.  Or the valves may need adjusting, which is possible I suppose but does not seem to me to be a misfire source.  
Another idea I have been considering is whether one of the multiple sensors, who's job it is to shut the engine off, is failing.  I think there is some merit to this idea as the engine, when started from cold, runs fine for about 20-30 seconds and then has a complete hard stop just like turning off the key.  It then starts up exactly as before, runs briefly and dies again.  After a few more tries and as the engine is warmer, it sustains a running level and continues fine albeit the intermittent misfires.
Another note, the spark plug looks fine and has not been replaced.
The gas is new but is winter gas here in New England meaning higher than normal ethanol.  My other older engines seem to do okay with this gas mix.
Thanks for any help.
Chris

Answer
Chris
Since you have taken the heads off, did you readjust the valves? Also when a engine heats up and then starts to miss it could be the coil, they have a tendency to break down when they get hot. Since all the other equipment runs fine with the fuel that you are using, the only thing left would be a coil the only way the timing can be off is if the shaft and the key way are stripped or not in align, have you hit something to cause the engine to stop hard like moving it and jamming the engine somehow. I don't see this in a generator but one doesn't know about someone else's equipment.I would check the coil to make sure you are getting a good spark after the engine runs and starts to break down, that's when you need to check for a good spark.