I managed to get the CPS plugged in all the way until it clicked. I took it for a spin to see if anything would happen. It drove fine for about 30 minutes, then just shut off. I tried jiggling/compressing the CPS plug, and that didn't seem to make any immediate difference. After a few minutes it started up, and I was able to drive a few minutes. Since I managed to get myself quite a ways from home, I had to go through this cycle several times. It shut off, nothing I do seems to help, but after a while it starts and runs for a few minutes.
I did notice that during the times when I can't start it, I can hear the fuel pump when I turn on the key just like normal. Also if I drain the fuel pressure at the fuel rail, then try to start it, and it doesn't start, there is more fuel at the fuel rail. None of this seems to point to the fuel pump as the problem, but I haven't been able to check the pressure yet.
I guess tomorrow I'll try to get a CPS from the dealer. I wish I didn't have to drive it for so long for the problem to show up...