Fresh fuel didn't fix it, but it really does sound noticeably better when it's firing, like sharper. Still dies.
I went ahead and ordered two new OEM camshaft position sensors, and a new OEM crankshaft position sensor. They'll be here Monday. I hope this fixes it, because I'm out of ideas. Next I really will need an oscilloscope.
BMW3-SERIES, you didn't say whether or not your car was throwing codes.