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form your description, your timing sounds spot on, and I can relate to how frustrating this issue is from when you know what you have. From this combination of issues, it seems to me that you have a lean condition as the secondary curcuit begins to operate. I'd suggest installing a step lighter secondary diaphragm spring, and should that not totally fix the problem, investigate what secondary metering plate you have, and an enlargement to the main circuit port on the plate. remember that drilling the plate is permanent.
another approach would be increasing the nozzle size; you'll probably want a #28 (0.028") nozzle.
couple of questions:
what size accelerator pump are you running? I'm sure a shooter size over 0.040 needs a 50cc so that the acc pump won't starve. The part number for the 50cc conversion kit is 20-11, and is a bolt on. the only accommodation that's needed is clearance when mounted to the intake(mock up to check for need of a spacer plate).
what position is your pump cam in?
The secondary plate will have a model number stamped on it that will cross reference to an main circuit size and idle circuit size, and will help you find the number should you want to try a different VS plate in your carb.
Example:
a '37' stamp is part number 134-37 that measures 0.073 main circuit hole and 0.031 idle circuit hole. the link below is a helpful reference for consideration. Holley Performance Products Catalog