Here you go... the cross hole in the needle connects with the hollow tip, which is now soldered shut (sorry for the poor picture). Turning the needle now actually has some effect on EGT, unlike before.
Seeing as this is the main jet needle and as you say, turning it in or out makes little or no difference on the EGT plus you have said that your plugs are gray, this all indicates that your engine is running lean, maybe. (I always thought that a proper fuel mixture would cause the plug tip to be light brown, but not according to NGK). See photo.
Are you using leaded gas? NGK has a description and graph showing how lead contamination on the plug can cause high rpm miss.
Of course this does not do anything to explain why your engine is idling rough. Perhaps the engine vibration at idle is causing the fuel in the bowl to foam up and cause fuel flow issues. Does you carb mount have a rubber connection similar to what snowmobile engine carbs have?
I do believe it's running lean, at least at idle; I suspect an air leak somewhere, which would have more effect at idle. I now have the carb off and am waiting for a rebuild kit to arrive. Lead, yes, I'm running avgas, but with only about 5 hours on the plugs I doubt lead fouling is the issue and I saw no evidence of it.