First thing I'd do is check the float. If the float is not "floating",
or is hung, the fuel pump will pump gas directly through jets.

Old Mopar products used to have a problem where the float was a
plastic material that would get gaslogged and partially sink.  The car
would run very rich and flood easily.  They kept making these floats
from same material for a decade or more :-(

A hole in a brass float, or corrosion or gum on float hinge is also
possible, or dirt in float valve keeping needle from closing all the
way.

Sunken or stuck floats, or float level set too high.

I get a similar problem every couple years in my Jeep with it's carb engine.

The fuel they now have seems to be bad for gumming up float needle
slides.  I need to pull my needle and seat out and clean them or kit the
carb every couple years.  It is the sliding area in the seat portion
that gets gummy.

At least on mine the needle and seat come out from the outside.  :-)

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
88 Cherokee 235 BFG AT's
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Droplets/dripping are a sign of something as simple as a vaccum leak
or the air mixture screws not adjusted correctly. If you've eliminated
those two, then your float is a little to high, the needle and seat
are bad, or has some dirt in it. Might want to make sure it's venting/
purging also. The float only has to be 1 or 2 32nd's to high to create
a problem. They are a little tricky to get just right.