The cause depends on what rpm or mph that the stumble is occurring. Also if the pull-off is weak or bad, it can cause the stumble. And since it is a '72 340 carb, the cause is easier to track down. What I would suggest from a mechanical standpoint would be:
fire off the engine, remove the air cleaner(keeping appendages out of the fan!)and push down on one of the air door dimples,
the air door should drop down .150"-.250" below the rear air door stop. If the air door has none of this slack and is tight against the air door stop, remove the pull-off linkage at the pull-off and bend the rear crook of the linkage a little bit rearward and re-install the linkage. This will give you a bit of needed slack in the air door.
Also the top of the carb should be casting #6-2007 or 6-2080. Tops do get replaced improperly over the years and can affect performance, David.