After just a few days, there should still be enough fuel in the float bowls to start the engine (briefly). Sounds like you have a leak, or something wicking fuel out of the bowl.
It's not unusual for the valves in the pump to leak enough to bleed the pressure in the lines off, but it should take only 4-6 engine revolutions (remember the pump runs at half speed) to have fuel spurting strongly from the disconnected line. If not, you may have a stuck valve in the pump or something.
Which might also explain your problem with missing at higher rpm. The pump will still move some fuel with one valve stuck open, but not nearly as much as it should.
Electric pumps are better in some ways, but certainly not a panacea for other problems. And overall, I'd have to say I've had more trouble per 100,000 miles with electric pumps than with mechanicals. Of course, that may be just because the Stags used an SU electric pump
PS the book procedure for testing the pump on the car is to disconnect the line from the carbs and connect a pressure gauge instead. Start the engine (on the fuel in the float bowls) until the gauge stops rising, note the pressure, shut the engine off and watch how long it takes the pressure to start falling. The gauge should continue to read top pressure for "a short time" (I love how precise that is!) and the top pressure should be between 1.5 and 2.5 psi.
Most vacuum test gauges will also read fuel pressure.
https://www.harborfreight.com/fuel-pump-and-vacuum-tester-93547.html