ONe thing to think about is your old fuel pressure setup from gravity feed is putting out very little presssure. You said your old set-up was 15 inches from tank to carbs, tubing size doesn't have an affect of head pressure so that doesn't matter. I think you need about 32 foot of water to equal one atmosphere which is 14.7 pounds. So one foot would be around 1/32 of 14.7 which is about a half pound. Your pump is putting out 4 pounds, so it's my guess you might be able to reset your floats for the higher fuel supply pressure, assuming you have floats? This might work if you have floats.
That fuel pump you have sounds like the fuel pump I had on my MG Midget. It actually had points inside of the pump that would activate a solenoid when the discharge pressure got low and cause a pumping action on the diaphram and again when the pressure bleeds off it would pump again. Never saw anything like that before until it quit working and took it apart, actually had to replace the contact points in the thing. That pump worked with the sidedraft SU Carbs on the MG, they were similiar to motorcycle carbs.