While I won’t argue that a facet electric pump is a good option, the original can be made to work properly. (I’ve got a facet pump on both our Imps, but I’m running the stock pump on my Alpine.)
Have you measured the fuel pressure at the carb to see what you’ve got while cranking? Should be at least 2psi.
What I found was that even after applying the rebuild kit to the stock fuel pump, it would not make the rated fuel pressure. It made LESS pressure after I put the rebuild kit in. The key to the matter was in the stroke of the pump. The arm which is driven from the camshaft, wears against the arm which pulls the diaphragm up and down. This interface point wears. Mine had little teeth ground into it where the very HARD material of the cam lobe arm wore into the softer metal of the arm which drives the diaphragm. The result was a compromised stroke length. If you build material up on the arm which drives the diaphragm at the point which it contacts the arm from the camshaft, you can maximize the stroke. I mig welded a bead on the diaphragm arm, and then ground a little away at a time until I JUST got a little bit of play in the mechanism.
Not sure if that’s the problem you’ve got, but that’s what I ran into.