Thanks for your reply. I'll give mixing a little fuel at a time a try. Didn't realize adding oil to a gallon of gas would make it go bad so quickly. 91 octane is the highest I can find and it would be a shame to have a saw that can't run on any of the fuel in the area.
As for the other potential problems, this particular saw has behaved like this since I got it a little over a year ago. I've taken it in for service twice with nothing but the fresh gas solution being uncovered - though the mechanic did grumble about the 365 being a particularly troublesome saw. When it runs, it runs great. Just wish I could get past this "works on Saturday, fails on Sunday" cycle.