make an auxiliary tank and then try to run it. if it works then it might be something in the tank or petcock. and if it doesnt work then move to the carb and look at it if it needs adjustment.
i dont understand your question because you said it doesnt work when its .4 gallons away from full and then you say it has to have at least .4 to run. the latter sounds like thats just the reserve. the first statement sounds awkward and i wouldnt know whats wrong.