Check the exhaust a little more. It sat outside, where a mud wasp could have plugged the exhaust up inside. I had that happen to a Stihl saw before. On another occasion I've hauled that same saw to my Stihl dealer only to have him dump the fuel, replace with fresh and start it up immediately. It's usually the simple things.
DING DING DING!!! We have a winner!!
I just now got done fighting with it for another hour...new gas (and one of those new econo gas cans that I now understand why EVERYONE hates!!)
Anyways, new gas, new plug, disassembled carb again... nothing!!!
I was beginning to conclude it was the fuel pump membrane although there are no tears in it, there is a ... "undulation" where it might be soft from wear.
Regardless... I then recalled my earlier comment about expecting to have felt some air coming out of the exhaust even if it wasn't firing.
I did not have a Torx driver long enough to remove the exhause...until today
I started to TRY and unscrew the exhaust and that thing is TIGHT!!! Wondering what to do... I for some reason simply stuck the Torx into the actual exhaust (remember, I've already removed the screen protector which I now see has a second use!)
Nothing came out BUT... there was a barely perceptable "something" on the tip of the Torx. At first I thought it was rust but it was not the right color...strangely enough... it was more brownish...
Then, bingo-rama... it hit me!!
No air coming out of exhaust, outside under cover for 1 week... those damndable daubers ....
After I pulled it out with just a touch of brown on the tip...I then pulled starter again. I could CLEARLY see some exhaust puffs come out even though it wasn't starting. This was when I knew I was on the right track. I had just broken the blockage and now the engine could breathe.
Put parts back together and in about 3 pulls the sputter was over and she was screaming away while I was adjusting the idle screw!!
Interestingly enough, I had already peeked into the exhaust tip but I only did a minor glance, I speculate if I'd actually looked with a light pointing in, I might have seen this right off the bat.