Schraeder valve. After it stalls and you're checking fuel pressure, is the key off or on? If it's off, you're pump isn't running hence no fuel pressure. If it's on, can you hear the pump running? If it's running then your pump is probably good. Could be a bad fuel pump relay, bad regulator or clogged fuel filter. Possibly the fuel dampner, but I doubt it.
Also, the symptoms being that it shuts down when hot then fires after cooling down a bit sound like the classic overheated TFI. An inherent design flaw by Ford. The TFI ignition module is mounted on the distributor right next to the hot engine block. Inside the TFI are small electrical components that are heat sensitive. When they get too hot they tend to interupt the electrical flow from the PIP thus creating a no spark condition. A pretty common occurence on early Ford EFI 2.3's. Short term remedy is a new Motorcraft TFI. Long term is a TFI relocation kit. Here's some interesting reading...........
http://www.autosafety.org/article.php?did=1216&scid=185
First thing I would do is run codes to see if it's electrical. Next, make sure the key is on after it stalls and then check fuel pressure with a gauge connected to your schreader valve. If pressure is good, I'd test and/or replace the relay followed by the fuel filter and FPR. That's my $.02. Maybe Fastest4d will chime in.