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Does your carburetor have a screw type jet at the bottom of the float bowl? And did you replace this carb with an original Tecumseh carb or an after market one?
The adjustment screw on the side of the carb should be bottomed out. If unscrewing it a little smooths the engine out then you will need to run a stiff wire through the hole at the end of it and try to open it up a hair.
The adjustment screw that I am talking about is on the very bottom of the carb in the center of the nut that holds the bowl on
Ok then lets take care of both jets. The nut in the bottom center is your main jet. Remove it (pinch off your gas) and then use a small wire to run through the tiny hole in it (see picture) While you are at it unscrew the jet on the side and run a wire through that as well. Try that and see if it has smoothed out?
A very slight angle should not make a difference, if it is closed at all then it could cause this. It is strange that the carb runs better with the air box removed.
Does the engine run any better when you engage the auger, sometimes adding a load to it will use the excess fuel to smooth it out
It does sound like a rich condition, which is opposite the normal settings on a new carb. Have you tried backing out the jet on the side yet to see if this leans out the mixture?
Also you may want to look at the float and make sure it is level. if it is you may want to bend the tab so that is a little lower then level
I doubt very much that it is the ignition. These ignition coils are timed with a key that holds the flywheel to the crank. These almost never shear on a snowblower but it may have and is worth checking. I still believe that your issue is within your carburetor. I am taking a look at a write up on your carburetor and think it is at least worth a shot at reading. I noticed that I sent you a picture of a B+S jet, the Tecumseh jet will have 2 small holes, the only other issue it may be in your carb would be the main nozzle that is up inside the carb.
Take a look through this site and pay attention to picture number 5 and 13