Based on your description the pilot circuit is working fine.
It sounds like the main circuit is either not getting air or gas in the right amount.
After running to 3000 rpm, hold it and let it shut off, are the plugs gassed or clean?
If clean, no gas, if gassed no air.
Sound like no gas, either because the main gas circuits are partially plugged or the carb pistons/slides are not raising in the bores, due to binding or lack of vacuum to raise the carb pistons/slides.
This is most likely where the problem lay.
The mains are a straight shot right up to the venturi area of the carburetor so being plugged up would mainly be at the jet which is the restricted passage way and an easy clean.
Of course the assumption of it being a main jet problem falls fully on the expertise of the
(OP's)analysis.
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