You stated that your floats appear to be free but are the needle valves that ride on the floats also free or stuck closed? If they are stuck closed, your floats will move down but the needles will remain on their seats not allowing fuel into the bowl. Over time, some fuel will seep in. Once you start the bike up, the fuel is used but can't be replenished. Pull the bowl and turn on the fuel petcock to see if fuel drains from the needle valves. Better yet, once your bike stalls, open the drains on the carb bowls and see if fuel comes out.
This is assuming your fuel feed to the carbs is clear. I've seen fuel cause needle valves to stick in their holders over time.
