Sounds like a fuel starvation issue....which you have already mentioned...
You seemed to have eliminated potential restrictions from the tank to the engine.
In an ideal world, the next thing to check would be fuel pressure. Most likely, you do not have a gauge, so this will be a little hit and miss....hopefully hit.
If I understood correctly, if someone keeps squeezing the bulb, the motor will run fine.
If that is the case, then compression, high pressure fuel pressure is probably ok.
It appears that somehow the low pressure pump (which you said is new) is not either drawing enough from the tank (possibly air in the line) or the pump is not pushing it thoroughly into the vapor separator bowl or the float in the vapor separator is closing off before the fuel gets to the proper level.
It might be possible that the vent in the vapor separator is clogged. It is the hose that comes off the top of the vapor separator and runs straight up through a filter to the top of the engine. Most people do not change that filter and if it is clogged, it could impede fuel flow into the vapor separator. You can test just by pulling the hose off the nipple on the vapor separator and blowing through it....or even running the engine without it attached for a test.
The other possibility, although you said the valve clearances have not been checked.....
I asked about that, because if someone takes the valve cover off and is not careful when working with the adjustments, they can rotate the low pressure filter cam out of place. The result would be that the low pressure fuel pump would work, but it would not pump as strong as it should and the motor will only run at lower speeds. The fuel pump cam is part #10
http://www.boats.net/parts/search/H.../BF130A4 LA/CAMSHAFT CYLINDER HEAD/parts.html
Another possibility is one of the hoses on the engine could be slightly collapsed or an internal piece of the hose lodged itself in the intake of the vapor separator....slightly blocking the flow of fuel.
To check for air in the line....get a short piece of plastic hose and insert it in various places in place of some of the fuel line on the engine. If you put it between the low pressure pump and the vapor separator and there are no bubbles when you throttle it up under load, then it is not sucking air....and you can go to other things. If there are bubbles.....then move it along the fuel lines on the engine back to the tank, until the bubbles go away. Then you will have located the problem.
It is just going to be a process of elimination until you find it.
Mike