I still say it is likely to be a bad crank shaft position sensor. When mine failed it often restarted itself based on road speed and still being in gear. Even when it didn't restart on its own, it would usually restart right away as soon as I pulled over and got it into Park. As the sensor degraded further, it got to the point where the car sometimes would not start for 15 or 20 minutes, but that was after I had been having the problem for a month.
That was the first time the CPS failed on my car. The second time I was driving home last new year'* eve and out of the blue the car stalled. Pulled over, got it into Park, and it restarted. I put a new CPS on 2 or 3 days later (as soon as the parts stores were open) and never had the problem again.
Your description of the car running and shutting off after 10 to 15 minutes is consistent with a CPS failure.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)