Not familiar with the Honda, but is there any chance:
the jets are clagged;
the emulsion tube is clagged;
the fuel cut solenoid is losing a signal;
the bowl vent solenoid(s) is losing a signal;
the delivery tubes in the amplifiers are clagged;
the mixture screws are wound out too far;
the fuel cut pressure sensor is faulty;
the power piston is staying open (wrong vacuum hose connected);
the bango on the pump is clagged;
the fuel pickup in the tank is clagged;.......
Can you tell if there is fuel in the bowls e.g. does pumping the accelerator keep it going?
"She gave me a look only a mother could give a child."