galene lakes trail is the worst possible way to get to the toothpick. as you would have to go over the d.tongue and descend
either go in by maselpanik cr and drop to international glacier, make quick first ascent of n. face couloir (if still icy and not melted out) to u-shaped notch then up standard route, or, approach to silver lake by standard route (via depot creek, one long day) then easily up to u-shape notch from south side
don't forget to post a tr!