Couple of comments, don't know if they will help. First - Went through a similar situation with my 76 Midget. A few different things compounded it. Dry (or appearance of dry) fuel filter - Not necessarily a problem - mine runs with about 1/4 - 1/2" of fuel in the bottom. Remove the fuel line from the carb, run it to a can, is fuel delivered? Attach a pressure gauge, what is the delivery pressure?
Fuel pump - New is not necessarily good. I replaced 3 before one worked. Again is fuel delivered to the carb and at what pressure? Heat shield - don't know how critical it is on a Zenieth - replaced mine with a weber - No heat shield and on the advice of Weber tuning, I did not attached the coolant heating line to the manifold.
To continue with the fuel system - my fuel delivery now became intermittent. Two other things to check - Is your tank ventilation system plugged or restricted? Restricted will cause it to run fine until you get on the gas for a distant and a vacuum builds in the tank. When was the last time you replaced the charcoal in the canister, or have you converted to a vented gas cap. Last but not least - What is the condition of the inside of the tank. Rusty? have some larger junks? The suction pickup line has a fine screen covering it. If this is plugged it will restrict flow. I ended up removing the screen, and cleaning/coating the tank. Caution it is a bit** to remove the screen and once removed, you should put a filter on the pump suction. That should take care of most fuel delivery items (oh ya, clean, blow out, and or replace the fuel line. It is small and can be kinked or partially blocked).
The ignition comment is also something to look at, you said this happened when taking off from a light. When stopped, the heat concentrated under the hood. A weak ignition system will give very similar indications, especially a weak coil that is starting to break down.
Just a few observations and personnal experiences.