Hesitation

As for a hesitation.
If the car hesitates with a slow throttle tip-in, that is called a hesitation or tip-in sag. Almost invariably, this is caused by a failure of the Transfers to respond in a timely fashion; usually because the throttles are too far closed.
as for a stumble
if when you whack the throttle from a dead-stop, the car stumbles and dies, that is called, oddly enough, a "stumble".
as for a bog
If the car stumbles, does NOT die, then goes; this is a bog.
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Now:
insufficient advance has nothing to do with any of these. I can set your 340's Idle-timing anywhere in the window from 5>15 degrees, and on a combo that did not bog, this action, by itself, will not create a bog.
However,
TOO MUCH Idle-timing, like 15>20, will cause the Idle-speed to rise, usually higher than most guys like ....... so they close the throttle with the speed screw. This closes the transfer slots to nearly closed, and the engine goes lean and idles like crap. So the guy richens the Idle mixture screws to the max, and so, it idles OK.
But, with the transfers so far closed, and with the Idle-vacuum so low, they are reluctant to get moving, when you open the primaries, and so, you get a hesitation.
If the convertor is tight, you may get a stumble or a bog.
So long as
the Ignition-timing remains excessive, you can dic around with the carb all day, and that tip-in sag cannot be cured until the Transfers are opened up some.
Whereas
a stumble can usually be cured by accelerator pump timing
Whereas a bog usually means that secondary air speed is coming in too soon. or is dry.

As to the points;
If the car starts, runs, and revs cleanly to 5500, I wouldn't be in a hurry to get rid of them. Usually the factory lifters start pumping up about 5500.
However, not a chance would I run points, on a DD.