Do you have a pic of the fuel pump? I have used a powerjection iii (I know shock and horror but it worked for me) and switched to a Holley Sniper recently.
I would like to see how the fuel pump is wired up. I would be inclined to run a switched 12 volts straight to the fuel pump and make sure you are not fighting some strange fuel on demand issue. The other thing I would check is to get the car in air safely and put a multi-meter to the hot line to the fuel pump. Have some start it and watch and see if you are getting a voltage drop or loss after the pressure goes away. If power is controlled by the Atomic it may be cutting power to pump.
The fact that after a quick cycle of the ignition doesn't bring the pressure back really points to the power to fuel pump or fuel pump. Electric fuel pumps almost never lose the ability to pump unless they are clogged. Invariably what happens is the one way valve that holds pressure in the line between starts goes bad.
If you really want a carb the street demon is one of the best for just general driving I have ever run across. The summit carb is pretty solid too.
We might drive you a little nuts with suggestions

but there are a bunch of people on here with years of experience and most of us are happy to try and help.