Can fuel pump be bad with a constant 5-6psi reading?

I'm going to try unplugging the distributor vacuum advance first. I suspected it could be a problem because I thought it happened on my Charger too. I don't have a good vacuum pump or one that's affordable. I did the valve adjustment according to the Chrysler service manual, I think the specs were .010 and .012 but don't remember which side is which unless I look it up. But they were all within specs. I did it precise too, I divided the damper pulley evenly into whatever degrees it was and turned to each mark and checked the appropriate valves. The only valve clearance check I've done before that was on a 76 Datsun 210 and I don't remember it being as complicated. If it's a bad distributor that would be easy, because I can just warranty it out. I know it's something simple and annoying causing this. I know there's bad accelerator pumps but when I've gotten 3 remanufactured carbs within the last year from the same company I'm putting that last on the list. I do see a good constant stream of fuel come out when I snap the throttle. It also starts up fairly quick and stays running even after a few days of sitting without starting. Like it starts up and stays running on the second try.