I was out there today doing some tuning....
OK, when I hear that, I think that the plugs have a bad gap on them, causing them to foul on the acc pump. In addition to the plug gap, This can also be caused by a marginal coil or wires, a confused rev limiter (if it's a 6 al pull the pill), or incorrect rotor phasing in the cap. Don't discount something stupid like moisture in the cap or the cap not seated 100%. When you get on it at low RPM, the load the ignition sees is the greatest - so any easier path the current will take. Light load won't always show ignition issues.
OR
The floats are too low
OR
the secondaries have debris in them.
OR
The secondary acc pump is too big (too much fuel) or the secondary spring is too light ( I missed if it's a DP or a vac).
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You also could be having lifter issues if you have a hyd flat tappet, see if changing the weight of the oil changes where it happens at.
What is your gap set at (set to .045) ?
What plug wires are you using?
Have you separated the adjacent firing cylinders (example: mopar / Chev 5/7 ; Ford 3/4)
Have you verified the cap is dry and on 100%
All plug wires are seated?
The plugs are tight?
The wires can't and aren't arcing somewhere?
You have a reasonable acc pump cam(s) installed (white / pink) , and not some mondo squirter size (.028-.035)?
Jetting is near stock for the carb?
Fuel pressure is OK, floats set to sight glass?
My dual carbs want a .035-.037 squirter and pink cam. Not much pump shot cc wise, but all of it immediately.
Jets seem to get too much fuel for too long on the acc pump if the carbs are left stock - no convertor or gear to contend with in a jet, so they don't need as long of duration - if this happens to be when your secondary acc pump starts (and you have a dp) - you may just have too much fuel for too long of duration at that point.
I'd have to hear it to be sure though, these are just some things that come into my head.