I know im not the only one to have this issue - i would start there first.

On a side note, we run as low as .015 gap on our Superjets when going out in the ocean, to help combat misfire since saltwater is conductive.

I just went through this with a new out of the box Holley on my 57 bird. Like was mentioned before, the plate screws were loose and both needle jets had bad o-rings. That corrected it works great now. Lucky for me the Holley is as simple as it is. When in doubt go back to the factory settings of 1.5 turns out on the idle screw and start from there.

I have a lack of knowledge about Holley carbs but..

Isn't the screw an idle adjustment?  Does it make any difference in the way the engine runs?  An idle screw should provide a significant difference from all the way in to all the way out, assuming everything else is within reasonable operating parameters.  In the case of my Edelbrock, the engine will not keep running if either of the two idle screws is turned all of the way in - this is normal.  Too far out and it starts running funky.

According to the plugs, how is the engine running?

At first it sounded like the accelerator pump adjustment but with the additional info it's leaning more to a problem related with the carburetor internals and specifically the gasket between the metering block and the main body.  But check the accelerator adjustment first anyhow as it only takes a minute.  At full throttle, there should only be ~0.015” of clearance remaining at the adjustment location before the diaphagm itself is in a position to bottom out.  If the accelerator pump linkage is loose or sloppy in the idle position, hesitation issues will come to the forefront.

If that checks out okay, then check for the power valve bottoming out in the power valve cavity and not allowing the metering block to fully cinch down on the metering block gasket.  Also check the main body where the metering block mates up to it to insure it’s not warped.  Just take a straight edge and check the main body in both diagonal directions across the face of it.

Ignition timing being too far retarded or the vacuum advance chamber not working will also create some off idle hesitation issues but your descriptions points to a lack of fuel or leaness as you lay into the throttle after you’re already moving.  Does the engine slow down at idle when the vacuum advance to the distributor is unhooked?  If so, then you’re either on direct vacuum to the distributor or as uncleaud brings up, too much transition slot is exposed in the primary throttle bores at idle.  But check that the mechanical advance is working anyhow.

You could try spraying carb cleaner around the carb while idling.  If speed changes, you know its a vaccuum leak and not an issue with jets/power valve, etc.

Mark.  I’ll have to disagree with you on this one.  The rule of thumb for power valves is to insure that the opening point for a power valve is at least 2 in/hg below the manifold reading at idle.  With an automatic transmission, this means taking the manifold reading with the transmission in ‘drive’.  A #65 power valve opens when the vacuum drops below 6½ in/hg.  A number 85 power valve opens when the manifold vacuum drops below 8½ in/hg.  Don’t know who originally started the misinformation regarding using a power valve that’s ½ the manifold vacuum but its definitely all over the web now and is not the correct way to properly tune the power enrichment system.  Each combination will vary somewhat in power valve requirements but the #65 power valves are generally a good fit in most applications as they will remain closed until the manifold vacuum drops below 6½ in/hg.  In rare cases, a power valve with a higher opening point will remove a surge condition that can occur in some cruising and light acceleration situations.  Hence the different options for power valves.  And for those that really like to tune, there are ‘staged’ power valves with two stages or metering for two different opening rates.  Many of the oem equipped Holleys for the trucks had these 'staged' valves.

Another thing to remember about power valves as that their opening rating will change as they age.  As power valves get older, the diaphagm stiffens thereby making the rating artifically higher or opening at earlier or higher vacuum rates.  At rest a power valve on a non-running engine is open and as soon as the engine starts, it closes.  An aged power valve can eventually get to the point that it will not close at all.

I got the info about power valves from the Holley Performance catalogue."If the vehicle has a manual transmission,take vacuum reading with engine thoroughly warmed up and at idle.If the vehicle is equipped with an automatic transmission,take the vacuum reading with engine thoroughly warmed up and idling in gear.In either case ,the power valve selected should be 1/2 the intake manifold vacuum reading taken.EXAMPLE:13"Hg vacuum reading divided gy 2=6.5 power valve.If your reading divided by 2 lands on an even # you should select the next lower power valve.EXAMPLE:8"Hg vacuum reading divided by 2=4.Since there is no #4 power valve you should use 3.5".I would think this is what is being picked up off the internet directly from Holley.In Nat's case he has the 8.5 power valve.Is possible the valve is allowing too enriched mixture too soon?I seem to recall his motor is completely stock.When I installed my 390 CFM Holley last year I had to increase the main jets to #54 not 56 as Nats is equipped with.The power valve on mine is #65(6.5).I have no bog or hesitation during transisition from off idle until the powe valve opens up.I am sure my 56 Fairlane is a heavier car than Nats T-Bird and doesn't need fuel sooner than when the 6.5 valve opens up.Maybe he should try to jet one size smaller and change the power valve?I am sure Nat is pretty frustrated at this point.If you recall he bought (I think brand new)carb which he has now because the one he paid to have rebuilt didn't work properly.Is it possible that the carb(s) are not the problem and maybe something mechanical is causing the problem he is having?If I recall some of the symptoms were similar to last time.Maybe something like the ground wire inside dist losing ground when the advance starts moving?

Because of the second gear start - mine is very sensitive to idle speed. Raising it 50 revs got rid of the hesitation - but puts too much torque against the converter to suit me when sitting at a light. When I drop it back - you have to put an egg under your foot. Starting in low  - no problem.

What was the original problem which made you think the cause was the carb?I know you had it rebuilt and were still having problems and decided to replace it altogether.Are you having any of the same problems as you originally did before starting on the carb rebuild/replacement?It is possible that the cause is not carb related at all.If you don't have a timing light you can't check where you are as far as timing and also cannot tell if the advance on the distributor is working correctly.You should  at least check the vacuum advance by putting a length of hose on and applying a mouth suction.You should feel resistance which means the diaphragm is intact.If no resistance the advance is not working properly which can give the symptoms you are asking about.In order to "read" the sparkplugs you need to drive at various speeds for a distance.Simply running short distance or idling will not give accurate feedback on plugs condition.As a suggestion it may be worth your while to have a professional autoelectric shop run a scope test on the motor and see if you don't perhaps have a problem with the ignition breaking down.As I think I mentioned last  time there is a braided  copper ground wire running from the breaker plate to the distributor body providing complete ground circuit for your Pertronix ignition.Check it and be sure its not broken under the breakerplate causing "ön-off"as the advance cuts in.Don't just look at it-pull up and make sure its still attached underneath where you can't see it.

If the only thing you changed besides the carb is the coil have you(A) tried the old coil?(B) Have you checked to make sure its not hooked up backwards as far as + and- to the correct connections?Are you running the balast resistor hooked up as stock because I believe the flamethrower is a high voltage unit that does NOT use the ballast resistor.Someone else on this site using that coil could verify this because I am not 100% sure about that.From what you told about the carb as far as jet sizes etc I don't think the carb is far off as far as settup.It should run well enough to drive it.I really feel you have a problem somewhere else like ignition.

While your mechanic is setting your ignition timing with a timing light, have him also check out the distributor’s vacuum advance system.  This can also be done with the timing light.