I had an 8 HP tec on a snowblower that did the same thing until I sold it to move south. I suspect it's BIG BROTHERS answer to cut air pollution w/ the fixed jet carb. I finally decided if it would do it's job I could put up w/ the idling antics. Sorry I can't help.
Mike

I haven't had the pleasure of cleaning one of these on snow equipment. Did you use a kit or at least rplace the bowl seal? I assume the main jet is in the bowl nut and special attention was payed in cleaning out the small holes. You may have to soak the carb in carb cleaner. However, every once in a while you can get lucky w/ jet spray cleaner and spray into the small passages in the carb venturi as it is running to the point of almost stalling a few times. Doing this you can draw cleaner up through the passages. It also cleans deposits from the intake valve stem at the same time.

I've been out of snow country for a decade. In my experience on the snow king was they would surge backfire if they were lean. I would think that to be the case if all was well last year and the problem reared its head this fall. Does this have a removable jet on the side? If so, many times forcing the jet spray into that passage when running as well will get the cleaner through the passage it needs to go too. Basically, if this is a standard Tecumseh carb except fixed- try my instructions. On many of the old style carbs they drilled the passage to the idle circuit larger then required and then reduced its size by inserting a pin, much like a roll pin to make the passage the correct size. Maybe yours was built the same. In itself, it isn't servicible. They did this as they were breaking the bits and damaging the castings when boring out the small passage. These carbs had welch plug on the side of the carb that covered a small mixer chamber as well as 1 well cover in the bottom end of the carb. You could if not succesful, carefully drill a hole in the side plug, pry out and re-soak or try jet spray. They used to suggest a dab of sealer (nail polish) to brush over the plug edge on this one once it had been installed.(Only on the outside plugs) Sometimes w/ Tecumseh the service carbs for the fixed jet come as adjustable. I don't know about these. Maybe the bowl nuts are the same size and the adjustable main jets would screw in and work. Wouldn't that be lucky.... How was the carb when you first dis-assembled it? If there were signs of water damage/ corrosion- the success rate of a carb rebuild just went down.
In your email you had asked about the possibility of a partially sheared flywheel key or a sticky valve. The jet spray should free up the valve if it is sticking. Keys don't tend to shear a great deal on snowthrowers, but yes it could cause your runabilty issue. If it ran well before it was put away last year, it is back to the fuel system or sticky valve. If you have other questions, post the spec # as well so we can see the carb (hopefully).Good luck!