OK. First thing's first. Let's establish that your secondaries are opening at the throttle body (base plate). There is a secondary stop on the passenger side of the carb that prevents the secondaries from opening if the choke is on. Take a look at the pics below.
Secondaries can open:
Secondaries locked:
With this in mind check the operation of the secondaries at the throttle body.
Next it is hard to get the airflap to open while revving in neutral with the choke pulloff installed. No, I am not advocating that you remove it. The pulloff puts deliberate delay on the opening of the air flap to make it more progressive and to prevent bog. If you can tap the airflap with your finger (engine off) and it opens (there should be a light spring tension) it's probably OK and opening under high load. It should open easily and smoothly with light spring tension. Sometimes the springs for the airflap break. If it doesn't feel "springy" that may be the issue.
Now for what I think your problem might be: If you hear the engine grow set of lungs my guess is the secondaries are at least trying to come on line, but can't do so because your POE is not functioning properly. POE (pull over enrichment) acts like an accelerator pump for your secondaries, except there is no pump, rather, the air stream draws fuel through a little hole (just above the airflap). It is not uncommon for the tube which feeds this little hole to fall out of the airhorn. Here are some more shots of the Q-jet I'm rebuilding to shed some light on what I'm talking about.
POE discharge hole:
Airhorn - what's missing here?:
There it is:
1
