The canyon ist not that wide (<1/2 mile). Assuming a speed of 200kts and the fact that they would pull max a 2G turn (probably even less) would bring them beyond the middle of the canyon when completing the turn into the canyon. (a = v^2 /r => R = v^2/ (2*9,81m/s) => Turn Radius R = 540 m = 1/3 mile.
This is wonderful in theory. I know only a tiny little bit about mountain flying, but one thing I have learned is that you do not get inside a 1/2 mile canyon below the ridges, and if you do then you stay on the sunny side, opposite to where the winds comes from and you slow down . There you might have a chance to make a 180 if the end is blocked, If you stay in the middle or on the others side , your turn will be far wider and part of it will be inside the downdraft.
As the Ziegler brothers former bosses of Air Alpes used to say : "it is far easier to teach to fly to a guy that know mountains , than to teach the mountains to an experienced pilot "