If there is fuel at the squirters, there is some fuel in the bowls. Next time it happens, open the sight plug and judge how much fuel is actually in there. If you can see the fuel, there is more than enough for the motor to fire, and fuel delivery to the carb would not be the issue.

Is it possible that fuel is leaking from the carb and flooding the motor while its parked? When it is hard to start have you tried putting the pedal to the floor and crank it (to clear a flooded condition)?

I know you said the carb was recently rebuilt but is possible that there is piece of schmutz in an internal passage? Perhaps something is blocking the fuel flow somewhere in the idle circuit.