It's unlikely Inmarsat kept anything but the last ping, but perhaps a US spy satellite logged all of them?
Hopefully... but it wouldn't have the time of flight measured for a call and reply signal, so the location might not be up to much.
Maybe the hourly broadcast from the aircraft (in response to the satellite's call?) is precise enough in time to be measurable to 20ms each hour (or Inmarsat's broadcasts were snaffled up too). If both signals are heard by a Three Letter Agency, then the various times of flight should allow that all to be put together.