With the preface that I find these things take time to really know what has changed and what is just coincidence, I ran two tanks of canned fuel through the saw today and it was much improved. It still showed some signs of weirdness, but I don't know how much of that is something up with the saw, or maybe m-tronic (which I did not reset) still figuring stuff out.
Using the canned fuel the saw ran reliably and started as you'd expect, meaning primarily that I could start it in "run" after it was warm without doing anything other than pulling the starter.
However, for both tanks of gas, when I got on the throttle it'd bog for a split second before it'd spool up (which is unusual, but it did recover quickly) and it seemed to me like it was down on power. Just based on pitch of the motor I'd say it was running at 85% RPM of what it normally does at WOT, and it seemed to get bogged down easier than normal when cutting. But like I say, some or all of that might be m-tronic still adjusting. I am a little dubious that it'd take 6 tanks (or such) for it to get back to OK, but it's not like I actually understand what's in the firmware. I'm basing my experience with fuel mappings from 4 cycle automotive EFI which I know this is not.
The other thing is that after refueling, it did want to die when I started to get on the throttle after the first start, but I backed off the throttle, let it idle down, then slowly got back on it, and it seemed to figure it out and run as it had before being shut off.
It was another relatively cool day too, which I only mention because, that seems relevant.
But the short of it is that although I am still going to replace the solenoid since by all accounts that seems like a good idea (and I already ordered it), the canned fuel test seemed to be useful. We have two gas stations in town now, and I suspect the one I was going to might occasionally get some crappy gas, so I am going to start using the other place to see if maybe that's in the mix (so to speak). I'll likely run some of that gas through it before I get the solenoid, so I may be able to make some conclusion about the alternative gas, but yeah, lots of hand waving. As long as I get the saw working better/reliably, I'm good though.
Andy