One thing I havent seen mentioned is the filter? Did you run the same filter? Was it a new filter when built? Clean it well during the trouble shooting process?
I could see where along with the ring finding its spot in the jug, the filter continually gets dirtier pulling more fuel. I would think it would take several different issues to empty that side of the carb in a progressive fashion.
Not to sound stupid, but have you replaced the fuel line?
I know it's a long TL;DR first post and bunch more to read after that but...
Yeah the filter and fuel line was mentioned as checked off the list early on and still more after that.
Most everything typical to this sort of issue was done with a great deal of redundancy over 3 years of... AaahrrrrR....!
One of the first things I do in this type situation, is disconnect the line from the carb and slip another larger/smaller long piece of clear line over/in it and blow through to get an idea of how well it flows. If the filter isn't particularly restricted the line shouldn't be collapsing but if I'm suspicious at all I try running it without the filter.
Then draw fuel up through the line while wiggling the tank around and look for bubbles, most important part here is not to drink any gas, lol.
Ultimately in this case I changed the line anyway, maybe more than once considering how frustrated with it I was getting over the years.
I sometimes try a version of the trick Randy just posted but with just long piece of filled up fuel line off the carb.
I guess you could say it did more or less "take several different issues to empty that side of the carb in a progressive fashion",
even though the fix was one simple thing.
The needle seat was restricting an ever increasing need for fuel as the saw broke in.
What really surprised me was that I first doubled the area of the hole in the seat (.037" to .046) and it still wasn't enough.
I'd have to guess that even though the hole/area was doubled, the way the needle taper sits down in the seat wasn't.
Out of curiosity I'm tempted to drill another carb but only part way down to see if the seat area itself is the real restriction...
Not enough time in the day dammit...