Damn Gremlins are impossible on this thing.

This is a 2004 GTP

I can get it to start randomly. It will run just fine once it's started. I'm sure it would run the entire tank of gas if I let it. But as soon as I turn off the ignition it will not restart. Typically it starts enough every time to kick out the starter and dies right away. Over & over until the battery is done or I give up. I might come back to it the next day and after a couple prime cycles it will start again. And not restart after I turn it off. I did get the P0336 code again as pending when it was running so I replaced the crank sensor again. Didn't fix it.
-I've cleaned all the grounds, the battery cables, checked all fuses & swapped relays, unplugged & replugged in the computer about 5x to clean the contacts.
-Tried starting it without the MAF plugged in.
-I can see the MAP sensor working when I crank it watching my Torque app (same for rpm & temp, I can also watch the throttle percentage if I step on the pedal).
-It has 60psi of fuel pressure at the rail.
-I've had the ignition module checked and it's fine.
-I've checked the signal from the crank & cam sensors with a multimeter while turning the engine over by hand and checked spark with a timing light on each coil. All works.
-I've disassembled the key to remove the transponder to check to see if the PK3 antitheft system is working correctly - it is, won't crank when I move the transponder away from the ignition switch.

At this point I'm absolutely out of ideas. The only direction I know to go from here is replace the computer. I don't understand how the engine will run perfectly fine when it runs but not start otherwise.

Thanks for all the suggestions so far. At least I'm not losing my mind, yet...