340 has me stumped

What I would do:
Let it stall! Quickly open the bonnet & activate the throttle lever & watch for a fuel spurt from the acc pump nozzle into each pri throttle bore. Also check that the boosters are not dripping.
If you get the spurt, it is a safe bet that the fuel delivery is ok.
Dripping boosters means the fuel level is too high in the fuel bowls. Could be leaking needle & seats, or fuel pressure too high. These carbs can withstand 10 psi, despite some BS to the contrary. Since you have tried a number of carbs, it is unlikely to be an internal carb problem.
If the above checks out, I would look to ign.
Get a small 3w lamp like a dash light. Hook one end to coil [+] & ground the other end. Make the wires long enough so that you can have the globe sit on top of the dashboard. Drive the car until the problem occurs. If the light goes out, you are losing power to the coil. Repeat the process, but connect the lamp to positive side of the ign module.

If all the above checks out, I would replace the module. There is a bloke, Dave Ray, on the net who reckons he has 55 gal drums full of dead Pert modules.