I might take slight exception to Larry's advice about any tech with zillions of hours on carbs. that person will be able to fix the problem but it will take a MB zenith expert to possibly do it at a price that doesn't resemble medical research.
From your decription you aren't running on the idle system. Look down the throat of the carb. Can you see gas when its running coming from the main venturi (you probably can)? You should not see gas coming from the venturi at idle, absolutely NONE!
Idle is affected by a number of conditions on those carbs. One is they have electrical solenoids shutting off the flow - verify. Two the secondaries are vacuum operated and often stick partly open. Destroys idle. Third, like all carbs the idle passages are the smallest, easiest to plug passages in the carb. And fourth the idle circuit passes through the top cover for an air bleed. The top cover is unvariably warped on these carbs and the top gasket doesn't seal the area around the airbleed. This in effect makes the airbleed vastly bigger and the result is that only air is pulled through the idle passages. This can be fixed by either sanding the top on a piece of flat glass (till the area around the airbleed is cleared) or by double gasketing the real bad ones. To do this I cut the center section out of a second gasket as the center is the area that is raised.
There is every bit as good of a chance of making the zenith run as an old weber. The JAM kit seems only a problem due to money. If you are thinking that other used junk is an alternative you will be faced not only with old carb problems but the problems of re-engineering.
Bosch Master, ASE Master, L1
33 years MB technician