I had a hell of a time with the accel pump plunger on mine one time. Even with a new plunger, it would not squirt enough gas. Ran similar to what you are describing. Sometimes new plunger will not expand enough, even with gas. Cheap kits do this most commonly. I finally got it to work, but I had to massage the leather and soak it really good in some light oil. Then put it together wet with oil. Stayed working after that.
Otherwise, without the AP, it will be hard to start. The squirt, with a good long push of the linkage is actually pretty forceful, and will almost turn to mist with a real hard fast push. The plunger will actually empty the bowl in a few good strokes.
It won't idle worth a damn if you have a vacum leak, or the idle selonoid is not working. Will idle good with choke, but not hardly at all without choke.
Also on the AP, there are several checkballs in most kits you get. If you used the wrong sized one in the opening in the bottom, then it may allow fuel to backfeed into the bowl, and not out the little nozzle when pumped, that is, if the pluger is actually sealing properly. The ball I speak of, is at the bottom of the plunger well, under a "G" shaped retainer. Unless it looks gunky down there, you may not have removed it.
I bet the plunger is not sealed properly. Will it accelerate very slowly? The AP is needed, but opening the butterflies slowly will induce the high speed curcuit due to vacuum. On a flat road, it will still run without the AP, but badly.
I have taken the top of the carb off on the vehicle many times, you can do this to get to the AP plunger, without taking the carb clear off.
