At this point, it seems pretty clear that
something must be keeping the float valve from closing properly. I see the list as:
- Leaky float body
- Worn needle valve seat
- Worn needle valve tip
- Incorrect float height adjustment
- Dirt in fuel keeping valve from sealing
- Fuel pressure too high
- Float binding on something
- Incorrect float and/or needle for carb model
You've already eliminated 1-4.
To test 5, you should try to run clean new fuel from a portable tank, with a new A1 rated fuel hose straight to the carb. Placing the tank a few inches above the carb will provide enough pressure for a gravity feed.
For 6, if you have an electric fuel pump, it may be the wrong model, providing too much pressure. This would overwhelm the needle valve and cause a limited amount of gas to overflow after stopping until the pressure bled down, instead of dripping continuously. This seems to match your observations. A pressure gauge right at the carb will tell if this is it.
7 is getting to the "grasping at straws" category. Check for excess gasket material protruding into the float bowl. Another possible cause of binding might be the little spring clip on the float end of the needle. You don't really need it and can leave it out upon reassembly.
8: Is it possible you have a slightly different Zenith carb model than the rest of us, and the float doesn't fit it properly? (beyond grasping at straws!)