My snowthrower starts easily. As I move the choke control to run, the engine runs smoothly about half way to full run. If I continue advancing the choke control to full run, the engine backfires (see flame coming out the exhaust). The engine power oscillates.

Hi,
The engine is, I believe, a Chinese knock-off of a Tecumseh OHV engine. At any rate the carb overhaul kit is part @951-11021 available from an MTD dealer. All the part numbers seem to be MTD. The manual can be downloaded from:
http://www.searspartsdirect.com/part...entId=1108380P
And the parts breakdowns begin at page 26.
Peace,
Clarke