Have no idea if this would help, I just had a similar problem and it kept throwing in the same fault code, I scoped the signal right to the PCM (behind the dash)eventually it was traced to a bad connection on the PCM multi plug, the hot start throws me off a little but you would still see a crank sensor signal even if the PCM is not receiving it.
give the connectors on the multi plug a yank while it is running, see if it stops or if it will not start.
might be miles away but it may help, crank sensors are really common as well and cheap.