MountainBob,
It's sounds like you've already got a good sense of those two sections. The chute is more exposed than the section left of the couloir. I have a picture of the couloir at
http://www.summitpost.com/mountains/phot...r_by____limit__(sorry, I couldn't shorten the URL). There's plenty of good scrambling up the rocks on the left. The chute is full of great climbing routes and the use of ropes can add a factor of safety if desired.
In either section, be careful of rocks knocked loosed naturally or by climbers above (and, of course, be mindful of climbers below you, too!). Helmets would be a good idea. You just never know. If you're going up to the left of the couloir, keep in mind that you're getting close to the East Face wall and a rock falling from there can fall a long way.
Hope this helps some. Have a great climb!
gosc