There's another recovery factor that happens to be present in this particular accident that I've been wanting to discuss.
In this case, the cabin pressure started to decay after the engines shutdown, as would be the case in many types. So how long can you stay at altitude in a glide before you have to get down lower to restore cabin pressure and O2? In this case, APU start at 30,000 could have provided a better engine restart option. Could it have provided cabin pressure as well on this type?
Ah, the conundrum of high altitude engine shutdown. Avoid hypoxia, preserve your glide to a good landing spot, and preserve your engine restart options. All at the same time.