Quadrajet runs better without accelerator pump.

[NathansCorvette]

According to my notes, there are not big enough differences between 7044502 and for example 7044211 to cause the symptoms you are experiencing.

A too large inlet needle valve seat combined with too high fuel pressure will raise fuel level in bowl and start fuel delivery sooner than intended.

My 350 still has the original fuel pump, and all the fuel lines have been replaced with factory-style ones so I'm certain the pressure isn't high...

A new needle/seat was included in Cliff's kit and was installed when I rebuilt the carb. It did look different than the one that was in there. The picture shows this.

[NathansCorvette]

I'd start by looking at parts directly related to the problem.

Idle tube size?  DCR's, upper/lower IAB sizes, jet size, primary metering rod size, and the power piston hanger arms. 

Since the carb is not original and unknown origin it could be something as simple as the jets were drilled out, worn out, or too big for what you are doing.  Most carbs that come in here have bent power piston hanger arms leaving the primary rods WAY too high in the jets.

If the post is still present on the power piston check the power piston height.  Maybe someone bent the APT arm in the baseplate and the piston is too high.

Those carbs are known for being lean, especially the CA versions and on this new fuel there is no reason it's so rich right off idle that adding any fuel from the accl pump is causing a rich stumble......

I will take the carb back apart next week and measure everything and get back to you.

[Kenth]

My 350 still has the original fuel pump, and all the fuel lines have been replaced with factory-style ones so I'm certain the pressure isn't high..

You need to check to be certain, otherwise you´re guessing.
It has been reported that new "factory style" fuel pumps pumping out 10 psi or more, so you really need to test yours.

FWIW

[NathansCorvette]

You need to check to be certain, otherwise you´re guessing.
It has been reported that new "factory style" fuel pumps pumping out 10 psi or more, so you really need to test yours.

FWIW

Yes, you are right, I cannot say for certain that the fuel pressure is correct. I am confident though that the pump is the original unit due to the orange paint overspray on it from the factory.

I have a pressure gauge so I'll hook it up to the steel fuel line with a rubber hose when I have the carb off next to check out the jets/rods/etc.