Update: I drained most of the 1 year old fuel (Conoco 91oct, ethanol free, with Sta-bil) out of the tank and carb.
I wanted the freshest gasoline possible, so I went to one of the busiest stations in town and got a gallon of Conoco 87oct with 10% ethanol. Added Sta-Bil to it.
I put that in the tank, and the snowblower fired up on the first try! Hallelujah!
In 45 years of using OPE, I have never seen such a dramatic benefit from using fresh gasoline. It makes me wonder how fresh the ethanol-free premium gas is that I have been buying the past two years. Given its high price, it can't be too popular, and might be sitting in the underground tank for 6 months, for all I know.
Now I have to decide what method I will use for storage at the end of winter. Letting ethanol-free gas + Sta-Bil sit in the tank and carb during storage has not been working for me.