Seeing as how you’ve tried a larger sized shooter, then try the ‘red’ cam for the accelerator pump actuation.  Before doing this though, I’d go ahead and try the #35 shooter first.  And I’m assuming the accelerator linkage is properly adjusted?  This means absolutely no freeplay in the accelerator linkage at idle and at full throttle there should only be 0.015” travel remaining before the diaphragm is bottomed out.  Fuel float levels are also players.  If they are on the low side, then the fuel pickup for the main system is delayed and the secondary float level is just as important as the primary float level in this regard.  There is a fixed idle circuit on the secondary side that requires the proper fuel level for it to work and this circuit helps in keeping the fuel from stagnating by using it as an idle circuit in those instances where the secondaries do not get used very often.

If you don't set it up, the old answer was always "flood it with fuel".

Make sure you distributor is set-up right. Needs to have plenty of low rev advance - which then requires a top end limit of 36°-38°(thats mechanical - vacuum blocked). Basic tuning rule is set up distributor, tune carb to suit.

If you use ported vacuum source for distributor - design the curve to start at 14° and end as above. If you use live manifold vacuum - use 10°, top end as above - and then limit the vacuum travel to about 7° max. Both set-ups will run well with stock engines.

This has been my experience too (albeit with a mildly cammed 312), that the culprit was ignition more than carb. Over time I tried several dizzy combinations...including a '57 setup with both vacuum and mechanical advance...and ended up with the Mallory which has been rock solid. Used one very light spring + one normal under the distributor plate. Result: 39 degrees overall (15 initial timing + 24 advance), but plenty of advance early in the curve. Eliminated my low-end flat spot.