Do you have a reusable air filter?
Here's an idea....I had the exact same think happen on my Ford Explorer, It would just seem to fire then shut off immediately, I too check fuel pressure and it was fine (just like you).
The problem turned out to be a dirty MAF sensor, the oil from my recently installed cold air intake's filter was messing up the MAF sensor, I pulled it out, cleaned it with some brake fluid, put it back in and VOILA the truck fired and idled fine.
Worth a try, sounds like a MAF sensor issue to me.
Piper
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