Chokes open do not cause flooding. My first guess is the needle valves are sticking open causing the flooding. Clean the carbs.
These are very simple and relatively easy to clean. Get a can of carburetor cleaner. Remove the carbs from the engine. Begin taking them apart by removing the fuel bowls. If there is residue in the bottom of the bowl it is likely that some has migrated in to the carb's small openings. Clean the bowl. Next remove the main jet and the tube in which it is located. (Some carbs use the main jet to retain the fuel bowl.) The main jet may not show any dirt, but the small opening in the tube are likely to be partially blocked. Spray with carb cleaner and it may take a small sewing needle to clean these small openings. If you haven't already, remove the floats and the needle valves. Then take the idle jet and idle adjusting screw out of the cartb. Spray each orifice/opening liberally with carb cleaner. Let dry. Replace the needle valves and floats, then while holding the carb upright activate the float with your finger while observing the needle valve. If it hangs up while the float is pushed up then re-clean the needle seat. If it continues to stick you might need to replace the needle valves.
This whole process should take ~1-2 hours. Double that time if this is your first time. This simple cleaning process will often solve most carburetor problems. While starting the cleaning carefully remove the gaskets to re-install later. If they are damaged or damaged in the cleaning order a gasket kit.
I'm sure I missed a step or two, but they will be obvious once you get into your carb. The main point is that cleaning the carbs is not a complex process, so don't be afraid of it. It is also something so common that buying old motors usually comes with caveats to clean the carbs first...
