Art... WOW... I reviewed your site...
... and man, are you doing a lot of work.
Hope you can also enjoy the car as well.
As for the hesitation on start-up... I don't know your exact carb but if you have a MANUAL secondary, versus the VACUUM secondary... then that could be why.
The vacuum secondary is actually a manual also that is not allowed to operate until the car has reached operating temp and the 3 way valve allows vacuum to then allow the secondary of the carb to operate. The could be a whole bunch of stuff a issue here.
Another area is the vaccum advance... which in MOST cases actually (effectively) RETARDS so that when the secondary is opened, the engine is allowed to "catch-up" and then advance... and the stumble is eliminated.
All engines need to be warmed a bit... but this stumble would be noticed when warm also. The dizzy advance is also controlled by that 3 way valve and is not allowed to advance until the engien is warm also.
(The 3 way valve controls is a SMOG control device for the advance, carb secondary, and gas recirculating valve. I removed all my smog gear, corked up the coolant lines, rerouted the choke coolant line, and just routed vacuum to the dizzy after installing a manual secondary carb. Runs really sweet now. You could also leave the vacuum secondary carb on and just tee off the vacuum line to the dizzy and make it work also.)
Hope this helps... do check with us often first and we'll probably be able to save you some time, money and frustration!
Keep up the good work also!