Not sure if anyone's reading this, but I thought I'd share an update.

I bought a a jack and some axle stands (yay). I managed to remove my old crankshaft position sensor. I cleaned it, tested its resistance, and replaced it. Everything seemed OK. The problem didn't go away

Having seen just how simple the sensor is, I'm struggling to believe that the sensor is faulty.

My next best guess is that there's a piece of magnetic debris sitting on my flywheel. Obviously I can't remove this without a lot of pain and effort, so I wonder what the next best thing is.

If it only has a small effect, I wonder if I could either add a resistor in the path of the sensor or add a washer to make it sit a little further away from the flywheel. I'm hoping that either of those will deemphasize whatever is causing bad readings.