I'm sitting on the other side of the world, yet have nice tools at my disposal
I post up here some screenshots of what I believe to be the region, and general path, J went down. I think the map on the DM isn't quite accurate, and have included that same map here with what I think may have been J's actual route marked in blue.
I have experience being lost in the mountains, during a cold winter, and luckily found my way out before dark, otherwise would have had to spend a freezing night. I know the panic that sets in, and I myself had to overcome that in order to think clearly and determine the best course of action to take in terms of making it out.
I think J's thought process likely was skewed by several things, youth, thirst, panic, etc. I think his objective was the coast, it just so happens the path becomes impossibly rugged down that ravine.
I also believe searchers possibly didn't find him earlier because, well, maybe they said, surely nobody would have gone beyond this point!, or, there's no chance he'd gone this far, or even, what has been stated here recently, he was down in a crevasse where a rescue canine missed the scent, and searchers simply didn't rope down in there.
Nonetheless, for his family, I am relieved he has been found. Hopefully they follow through with some things, and there is no evidence of foul play.