You can "fight" that idle-to-WOT situation until you're Chevy Orange in the face and not get rid of it, from my own experiences. DO check the accel pump for an immediate pump shot as soon as the throttle is moved, but if it's a Carter, it'll probably not happen as quickly as a Holley might do that, by observation. No amount of swapping slots for the accel pump linkage will fix it, either. Been there, done that.
But do make sure the accel pump puts a solid shot when the throttle is quickly moved from idle.
Chrysler typically used torque converters which were a bit "tighter" than GM or Ford used, so that puts more load on the engine when the accel is opened too quickly, and the engine can't respond soon enough. Hence, the spit-backs, pop-backs, and such.
Go ahead and do all of the checks and such as you desire, to ensure there are no other problems that you might not know about. Timing, points and such, vac advance, vac hoses, etc. Just to make sure they are what they need to be. Then take it back for a re-check at the shop.
What led you to believe the carb needed rebuilding in the first place? The point is that if a rebuild didn't fix what you thought it would fix, everything was probably fine to start with. What you might need is something more than just "a shop", but somebody that knows about carbs specifically, but not some "hot rod shop" that makes "big claims".
Rather than idle-to-WOT stomps, you might well have better luck with 1/2 throttle punches and then WOT after the car is moving. This does a few things. First is that it keeps the vac advance working (advancing the spark setting), which keeps more advance in the motor until the centrifugal advance starts kicking in. With your WOT punch, all vac advance goes away, with no advance happening until the centrifugal advance starts. Not the best for lower rpm power.
It also keeps an initial over-rich condition from happening. Too much fuel too soon, not fully supported by increased air flow through the engine.
From my observations, some carbs and engine combinations seem to handle the WOT punch better than others. IF yours is one that might not, then don't do it! It might make you feel good to do it, but if the car doesn't like it, don't do it. Learn how to use "the machinery" in the manner it lets you know it likes to be used in. That's one lesson many people never learn, cussing the car all the while. You'll have more enjoyment when YOU and THE CAR work together, than if you try to force it to do things it doesn't want to do.
Just some thoughts,
CBODY67
