I don't know if you're responding to Dan, or my usurpation of his thread, Mike.
But if it's me, then that's not the problem. I can ease it into the 2000 rpm range at a snail's pace and it will run rough when I get there. The quest for the problem continues...
This post is quite old, but sounds like your running auto gas, ethanol will attack carb parts and the inside rubber intake seals, I seen it time and time again, My customers run Avgas and MMO stay away from that auto fuel of anykind,if you have that neoprene needle valve it turns it to mush. And leaves a rubber line on the seat. First sign will be fuel dripping off the carb on the floor.
There is a lot of advice in this thread. In other words several scenarios can cause your engine to stumble when the throttle is advanced. Elimination of each is the best way to troubleshoot.