Now, if, as it seems:
- It impacted the ground with landing gear "in transit"; and
- Full gear retraction takes approx 12 seconds...
Then the gear lever must have been selected UP less than 12 seconds prior to impact. Let's call it 10 seconds.
Hmm - the 777 gear "swing" time is about 12 seconds. But there is a
substantial delay between "lever selected up" and the actual start of the gear swing - fairing doors open, gear leveled longitudinally, downlock released. About
18 seconds total while the gear is still vulnerable outside the gear bay, after "gear up selected".
It impacted the ground near the far end of a 4500m runway...
It ended up near the end of the runway - that is not necessarily where it impacted. It probably slid quite a distance before stopping.
US Airways 1493
slid at least 300m/1000 feet
after landing on a Metroliner at LAX. Admittedly gear down - but dragging (friction) the wreckage of the Metroliner under the fuselage. And was
still sliding at a substantial speed when it hit an airport building and stopped abruptly. Conservatively, I think you need to assume "impact" was 300-500m prior to the final resting point.
Density altitude with 49°C temperature would make 120 on the gauge = about 130 TAS. But with a headwind, I'll accept 120 GS (and 10° pitch) as possible - at some point during the progression of the crash. Not convinced GS was as low as 120 kts at the
beginning of the GA attempt.
Combine those with the actual available runway between the displaced thresholds, and I think your assumptions and math need revision.