Johnny D
I suspect the NTSB will give us a definitive answer on the double Engine failure. Not me. I've been wondering the very same thing. And you're right, it wasn't part of the deal. My guess is the CF34 itself at high altitude in very thin air. With a high angle of attack to maintain altitude, (another of my assumptions) airflow over the wing might have disturbed the airflow through the engines. However, prior to any aerodynamic stall, you have automatic continuous ignition.
FL410 must be really, really close to the performance limit for this engine anyway. (Watch this space)
Possible scenario: (note: "possible")
The ADG provided ship's power till FL300 following the loss of both generators.
At FL300, the APU could have been started. Power restored. AP engagable. FMS back in business. Cabin Alt still slowly climbing cuz the APU can't provide pressurization above 15.
At 26,000 the aircraft is pitched down to accelerate to 300 KIAS + and at 21,000 the aircraft should be at 300 KIAS when the crew would confirm start parameters, select continuous ignition and start an engine. Depending on crew skill with the QRH, they might not have increased from 240 KIAS to 300 KIAS as stated in the re-light procedure. The core speed of the N2 wouldn't be much above 2 or 3 %, if that. Even at 240 KIAS.
Depending on the tail number of this aircraft, they needed 330-335 KIAS to conduct a windmill start.
Prelim info suggests the aircraft didn't exceed 300 KIAS which would explain their inability to re-start an engine above 13.
You would certainly expect at least one engine to have been re-started using the APU. But then, we don't know how the procedure was followed. Nor do we know how 'excited' the crew might have gotten as they neared low altitude, an airport and uncertainty. All we know is the result.
