Several years ago I had a car that did very much the same thing... Well for some reason I got the feeling I had a fuel pump issue so I pulled the line off the carb and stuck it in a gasoline proof cup, cranked the engine, got a trickle of fuel (not a jet like I expected) and a depression in the pool of fuel in the cup.. Like someone was blowing on it.. Yes, blowing on it,, through a straw.
Replaced the line from the tank to the fuel pump and all was well
The old line had about a thousand pin holes in it, not big enough to leak fuel, but more than large enough to suck air like a vacuum
Not suggesting it is your problem.. But what the heck, one more thing to check