When I have had such symptoms it was usually some dirt or deposits in the main jet, It is very easy to take the bowl off the carb while it is still mounted on the car if you are using the original type Zenith, dissconnect the choke/GAV rod, take out the bolt, and lower the bowl assy, if you look carefully at the jet tips you will probably see the debris, a quick squirt with some air, or carb cleaner will flush it out.
A slightly spread cotter pin can keep the sleeve and spring in place on the gav rod
There is another quick "on the road" sometimes cure for debris ---with the engine running --step on the throttle and close the choke for a second, or covering the air inlet with your hand as you snap open the throttle ---this method sometimes will suck the debris through the jet.
It is not unusuall to fine a lot of debris in the screens, and they should be checked often, some of our members here will post pictures of a debris trap they install , a dead end dogleg , and others use a standpipe in the tank .
I have had problems in the last 2 years with this new gasoline making a gooey deposit in the tip of the main jet causing your symptoms, but it has happened only if the car has been sitting for 2-3 weeks, I have had to change 35 year old habits, now I turn off the gas valve before I back the car into it's garage to lower the gas in the bowl.