What speed are you running the motor at when it sputters and quits? It sounds like it’s fuel related for sure being it takes off again with a blip of the choke. Does this motor have knows for high and low speed or low speed only?

If the tank vent is open and the filter is not plugged up, it seems most likely this is a carb issue. Make sure all the gaskets are in good shape too but my next recommendation is to pull the carb off again. You stated you didn’t notice any obvious debris in the carb when it was off. There is a high speed orifice screwed horizontally into the bottom of the carb bowl behind the drain screw. It requires a special tool or a slightly modified straight screwdriver to remove. These can become blocked or partially blocked and that blockage is invisible unless the orifice is removed.

Since your motor will not stay running at all at lower throttle settings, it seems likely you also have some blockage /restriction in the low speed circuit. These can often be cleaned without oulling the Welch plug on top of the carb but jot always. If you completely remove the low speed packing nut and needle you can use aerosol carb cleaner with the straw to spray directly into the low speed orifice. Also, there are small holes in the top of the carb throat directly below the Welch plug by thr butterfly. Spray carb cleaner thru those holes and make sure you are getting cleaner coming out at the opposite end of the low speed circuit. If you are not getting flow thru you will end up having to remove the Welch plug. Make sure the needle packing is holding the needle firmly and not allowing any air to leak by when running. I would suggest buying a carb kit and replacing the float needle and seat and the float if it is still a cork one.

The initial setting for the low speed needle should be around 1.5 turns out from ‘lightly’ seated. Itmis possible there maybbe another issue, but the carb seems like the next logical step considering the symptoms. I hope this helps.
-Ben