Thanks so much for the replies, this is all extremely helpful. I unplugged the upstream o2 sensors, no change. I replaced the CCV and seated the manifold oh so carefully, no change. Replaced the crankshaft position sensor, no change. (Throwing parts at it.)
Behavior is EXACTLY like in BMW3-Series' video. It will crank and not start, or crank and fire to about 750RPM with no gas pedal. If I hold the gas pedal all the way down, it will rev to ~2K RPM and dies.
I guess it is possible that a bad CPS (crank or cam) is giving a weak signal (but not bad enough to throw a code) and the spark and injector signals from the DME are intermittent. At this point I am wishing I could afford an oscilloscope. There are some on CL for around $500. I can spend that much throwing parts at it pretty easily! However, I think the intermittent ignition theory is quite plausible, because I was never able to get the car to stay running on carb cleaner.
I also agree with Joyism and BMWFatherFigure that it sounds like fuel starvation. But the fuel pressure checked out, and I already replaced the pump and filter, so I was starting to think the fuel could be very old -- I have no way of knowing how long the car was sitting. Today I was planning on draining the tank and putting in fresh fuel. But I don't know if that's consistent with that I couldn't get it to run on carb cleaner.
Gosh. It's just like the video. I wonder if I should just order up the CPSs...
Also, about the codes. I am using INPA, and I can get the codes. I had a downstream o2 sensor codes and a thermostat code, but I fixed them. Was the car in the video throwing codes?