Did you try readjusting the idle? The idle is affected by residual fuel lurking in the crankcase and the first time you run the saw at full throttle for awhile it cleans out the crankcase and the idle may need to be set again.
From your description, it seems to run good on the high speed fuel, just stumbles and dies when sitting at idle after the WOT run, a sign that it is now too lean at idle. If the saw runs at full throttle and full load (have to cut something) you do NOT have a problem with fuel delivery.
Do some testing, when it stops is the plug wet or dry and test for spark when it quits.
Yes. Once it started running goofy, I tried to adjust the low speed screw but it seemed to have no effect. When I first started the saw up it ran good and the low speed screw did affect how the engine ran. It kind of sounds like it's too lean, but no matter what you do it doesn't seem to affect it. I really think it has to be an ignition issue at this point, like something is failing once it gets warmed up.
It wasn't running at full throttle before, but it seems like after I cleaned out the high speed channel it would rev up good. It's just that now after it warms up it starts running poorly and then dies. Let it sit for a bit and it'll start right back up and run good again.
When it starts running rough, if I try to rev it up again to full throttle, it just bogs down and almost dies.
I agree, I don't think there is a fuel delivery problem at this point. I think there's something else going on.
I'm going to start with the condenser / points and if that doesn't work I'll try replacing the coil. It's clearly getting fuel as I verified that when the carb was apart spraying stuff through the ports. It has great compression. It has to be something with the ignition system. All the stuff in there appears to be original, which means it's over 60 years old. Probably time to replace some of that stuff.
Last time when it crapped out, I pulled the plug and it was pretty dry. Maybe a little fuel residue on there, but looked like a normal plug for the most part.