If the Stude has a vacuum tank, there may not be enough height differential between the outlet of the vacuum tank and the carb inlet for gravity to overcome the friction of the horizontal needle.
Carter used a horizontal needle valve on the BB downdraft carbs used on MoPars from c. 1934 through 1952.
Just about every US auto & truck manufacturer went to mechanical (or other ) fuel pump after 1932, so the BB-1 updraft applications for COE trucks (Dodge used this carb too) were all designed to operate on pressurized fuel systems.
And now that I went back and looked at your pics, I see a fuel-pump right next to the carb...
Would suggest doing a pressure-check on the fuel-pump; if you found that much crud in the float-bowl of the carb, I wouldn't be surprised if there's similar crud collected in the check-valves of the fuel pump, preventing them from sealing completely - this would allow some fuel flow, but not enough pressure to open the needle ?
When I resurrected my '48 New Yorker from a 20 year nap in a field, I had all sorts of issues during the first months of driving, stemming from "crud" in the fuel system, including debris catching in the pump check-valves, holding them open.
I was able to remove the pump, open it up, clean-out the crud, and get going again. On the side of the street, downtown, in mid-day traffic, in the rain.
The needle-valves I've seen that work with a clip usually have a groove machined in the float-end of the needle... if you're ambitious, and nothing else helps, I think you could fabricate a "hair-pin" spring to hinge around the float pin, one leg grabbing the needle-valve, the other leg resting against the tab on the float arm...
Check the fuel pump first.