Guess its time for a quick update. I went ahead and picked up a carb rebuild kit, and replaced the impulse line from the carb to the crankcase. Just an FYI, swapping out the impulse hose is an absolute PITA on this saw. I don't know if it is necessarily any easier on other saws, but it was aggravating to say the least on the 066.
I rebuilt the carb, and the arm on the replacement fuel meter lever is definitely sitting higher than the previous. The diaphragm on the replacement is also more pliable, but I am not sure if both of these will correct my problem. I haven't been able to test the saw yet as I managed to split the in-tank fuel line. I pulled it out to check it, and messed around and split the hose pumping air through it to check for leaks. I guess its possible the area was already compromised, not sure, but its now definitely fubar'd. Won't be able to get a replacement until tomorrow, so hopefully I will have some good news to report then.