The problem definitely sounds electrical. Its very typical of sensors and meters to do what you say is happening. It could also be a relay getting too warm.
With the list of thing you have done, diagnosis is getting harder.
Have you replaced the starter motor or the starter solenoid?
How did you get on with AFI?
I gave them a call, they basically said sounds electrical and could be a million things and need to see the car.... Im gonna go see a local Auto Electricion tomorrow and see if he has any ideas...