I see a slight tweak of the carb fixed it. (Your post #33)
You probably had to do a slight tweak richer. (maybe for a slight 4 cycle sound out of the cut)
But I've seen the fine screen in the carb restricted cause power loss, the grub screw vent not venting, old dried out carb internally.
I want to make sure that the engine is NOT EATING ITSELF while I'm trying to repair the saw or has not already got severe internal damage. (monitor it temp under load and look at the piston through the exhaust port)
That is a point I was trying to make. (engine leaning out and gets worse as it gets hotter under load and also the piston friction scuffing starts adding to the generated block heat) Most generally the carb is adjusted too lean, (H jet in just little to much, even 1/4 turn in on some saws is too much) but the Operator needs to be aware when he encounters a chainsaw doing as you describe that it can be ruined very quickly, scored piston and cylinder. I use a IR thermometer to verify that the saw is not overheating. If it's a new to me saw with those symptoms I remove the muffler and take a peek at the piston and if it's already scored, no need in proceeding, unless you just want to adjust the carb and see if that corrects the overheating issue. If you take the saw apart and replace parts and re-install the same carb and make tachometer adjustments the engine might do the same thing again fast. (and someone (new operator) not aware of such can destroy the saw fast by trying to force the saw to operate/cut correctly)
You might not ever notice lean and overheating when using the saw for trimming, on and off the throttle and the engine runs strong.