Interesting, I'm having similar no start issues. My WJ starts with a delay when cold, runs fine (replaced the injectors already and it runs much smoother since) and has a lot of power, however I haven't pushed it to its limits yet, so I don't know if it cuts out. The no (or extremely difficult) start occurs when I start from a cold engine and move the car just a few meters and turn it off. It starts when cold and starts when hot (with that delay though).
You're mentioning the filler cap, is there a known issue with those? Could this cause difficult start? I don't have a DRBIII, but I do have an OBDII interface, not sure if it shows HP though.
What does the fuel solenoid do? I would imagine if there's an issue with the HP side, the 'check engine light' would turn on? So I'm thinking air bubbles before or after LP side? Just a thought...