I climbed the West Chute in 9.5h round trip from South Lake TH; up & down about 3700'; descending via Green Lake. This route was better than I was expecting. The boulder field above the highest Chocolate Lake is decent. And it's cool being in the Chute - and the route goes straight to the summit.
I was able to avoid loose rock by climbing along the slabs on the left and avoided the temptation to head up steeper terrain on the right.
The start of the Chute:
A beautiful wall on the right:
About half way up (I'm guessing ~12,500') the Chute splits. I stayed to the right by 3rd-classing along an almost-horizontal slash of white rock. Further up at ~13,000 I encountered a permanent snow patch (August). Here, instead of heading left I climbed straight up steep-ish, good quality, lichen-covered rock to the summit ridge.
Just below the summit ridge:
The long descent over Vagabond and down to Green Lake took some shine off this direct route. I wish I had down-climbed the route. North of Vagabond at ~12,000' the terrain is loose with large dangerous bouders; be careful in this area.