Did you check fuel pressure in the morning or when it wouldn't start? With the car ideling the fuel pressure should be between 45 and 55 psi.
You may want to check the fuel pressure while it's acting up like when you have to give it pedal to keep it running. This will tell you if there is a fuel issue.
Is this what you've done?..cause 20 psi will not only cause a lean condition, it's not good for the engine.
If the pressure is in fact 45 to 55 psi when running then move on to what these other guys have suggested.
20 psi while running:
I understand why you asked about pressure at the pump but check the voltage at the pump first. It should be over 13 volts. If it's only 8 or 10 volts then you'll probably have to install a fuel pump rewire kit.
If the voltage is correct then I would suspect something wrong with the regulator. Did you remove the vacuum line when you "disconnected" the regulator?
I don't think this a sure-fire way to eliminate the regulator as a possible suspect.
Heat soaked electronics:
When you park the car the latent engine heat can wreak havok on many electrical components, ICM, CPS etc.
Hope this helps.