We just finished the Mountaineer Route yesterday (Sunday, 9-28). We camped at Iceberg Saturday night. I think this is the correct definition of the various stages of the hike from the lake to the top:
1. The Chute- the fan of granite from the lake to about one-third of the way to the peak.
2. The Couloir- begins at the top of the Chute, continuing on at a similar incline, but surrounded by granite walls on either side.
3. The Notch- a level spot at the top of the Couloir.
4. The Gulley- an immediate left turn from the Notch starts up the Gulley. This section requires a fair amount of class 3 to 5 climbing, with a lot of exposure.
5. The Traverse- continues nearly level from the Notch to the back of the mountain where one can rejoin the main trail for the final ten minutes to the summit. This section can be very dangerous due to almost year-round ice in a section that gets very little sunlight.
The trip really gets exciting from Iceberg to the top. We stayed to the left side of the chute. I went up the middle of the couloir where the loose sand and rocks allowed progress at a pace of about three steps forward and two steps back. At the moment the Traverse is ice-free, making it a much easier path to the summit than the Gulley.
Here's a winter view of the way up:

and how crazy steep it is:
