The double-action pumps shouldn't run at any higher pressure than the single-action types. Try putting a pressure gauge on the carb inlet line, and run the engine with the line deadheaded into the gauge. It should run for a short time on the fuel in the float bowl. Most pumps I've checked that way run from 3 to 5 pounds, and hold the pressure for a short time after the engine is stopped. That shouldn't be enough to override a float if it's working properly. I'm guessing the float is hanging up on something inside the carb, and needs to be bent or adjusted to correct the hangup. See if the "float drop" setting is correct, the lower limit of the travel of the float. It's just as important as the upper limit adjustment!
Jerry
