Ya know, you can spend a few weeks, and a few bucks on mystery fluids, and take it off, and put it back on, and adjust, and fiddle with it for weeks. Or, you can go on Amazon and buy a carb, with a shut off valve and start blowing snow in a few hours.
I am not generally a fan of throwing parts at it, but if the choke fixes the running problem, you have one of the small passages in the carb blocked. Most likely by detritus from bad fuel, or from some deposits of corrosion after the water in the fuel broke down.
So, buy this, take the old carb off, put the new carb on, insert the shut off valve in the fuel line and move on with your life.
https://www.amazon.ca/Carburetor-Sno...s%2C199&sr=8-6
When you are done moving the snow around, set the throttle to idle, and turn off the fuel supply at the red valve, and let the engine die. When you want to use it again, turn on the red valve, let it sit for 2 min to fill the float bowl with fuel, and run it. Lather, rinse, repeat.
The carb job is not hard, but pay attention to the throttle rod, and small spring, be gentle. Maybe replace the spark plug too, as your choked engine may have now fouled the spark plug.
Edited to correct carb PN.