OK, when you say the primer bulb was going soft, what does that mean ... It's either empty and squeezes easily, or it's full and does not. If it's somewhere in between, it sounds like the fuel pump is pulling a vacuum ... And that is not a fuel pump problem. It's a tank venting problem.
The tank is supposed to have a one-way vent that lets air in, but not fuel out. If it's clogged it could be all your problems ...
If you look at the fuel gage area on the tank, you will see the word "Drain" next to one screw. This is the one screw you take out to drain the tank upside down at seasons end. It's just a 8 or 10 - 24 machine screw. Take it out with the tank upright and go for a run. If all works well, you know it was a venting problem and can work on that. If it still tries to die, you have a weak fuel pump, or a clogged pick-up screen ...
To service that, you need to remove the fuel gage area (all four screws, and carefully lift out the gage and the pickup tube. Spray the screen end with brake clean and hit it with compressed air. You should be able to see through the screen. It's fine mesh and soldered on. So treat it with care. But it will clean
Put a little grease on the threads when you put that screw back in. Don't go crazy tightening, just snug is good
If you took all four out, put a little grease on the gaskets and the screw threads for now and re-assemble. Try the motor. If all good, you can get new gaskets this winter and fit the fuel gage/pick-up nicely when not boating