Ken would certainly know more about the A-4 pump than I from experience. However I still feel that a check valve may be weak. I installed on my boat and a few others a new water/filter separator with all new lines from the tank to the carb. By pumping the bale in 3 cases the pump pulled the air through and prime was achieved and then the bowl filled. Once the bowl filled the bale was stuck in the "Pump" position.
Dave Neptune