There IS a fuel pump, it's an integral part of the carb.
It's shown in the upper portion of the Mikuni carb diagram attached [notice the fuel inlet, pulse, check valves, and pulse diaphragm].
But, if you put on a NEW carb, all that sould be OK.
Twice, I put on a new carbs on my two '97 GTIs [720] and both worked great right out of the box.
I agree that it seems to be a fuel issue .. but is the issue in the carb? or the supply? the pulse?
CHECK the pulse line is secure [automotive fuel line, not soft tygon line -- as the pulse from the crankcase "powers" the fuel pump] Otherwise --
Maybe to "divide and conquor" - may I suggest, with extra fuel line [I use tygon] - rig a plastic jar, lid with two holes, half full of gas, such that the fuel supply to the carb pulls from the jar, and from the carb returns to the jar [thus bypassing the entire fuel supply system.] Start the engine, and see if it revs. If it revs ok from the jar supply, the boat supply is suspect. If it dies, then the carb / fuel pump / pulse is suspect.
If you rig your jar such that you can see the end of the fuel return line, you should see fuel dribbling back into the jar from the carb. [ if you are close to a body of water, preferably do this with the rear end dipped.]
Pic is of my "divide and conquor" jar [ it's a plastic peanut butter jar, with hole for line to carb supply, fitting for line from carb return.]
Sometimes this test can help isolate the issue to either the supply or the carb. /a
