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The symptom is "dies when pressing accelerator SLOWLY, runs when pedal is double pumped".
That indicates that the AP is working.
Idles OK, but has a hole when transitioning from idle to main circuit indicates a resrtiction in the idle circuit, or a problem w/ the beginning of the main circuit.
Probably dirt in the slow jet or the primary air jet.
Fix: disassemble & clean.
Where in Minnesota are you? Close to Poser? He's in Farmington.