No offense, but there's really nothing scary about that chute; annoying (actually extremely annoying), yes, dangerous, not really. I can see some injury from falling rock, but death slide/fall, no.
As Steve said, you should have gone up the left side. Look at the picture. Next time (if you come back), go where the dotted line is.
http://images.summitpost.org/original/193243.jpgIf your climbing skills are that advanced, you should have taken any of the solid routes directly to the summit and avoided the chute.
From the Notch, I'm shocked that you thought about doing the traverse as I always see that path as asking for it when there's any easy way up that wall most refer to as the Final 400. I'm also surprised you took the right side up as it's usually full of ice. The left side is chock full of SOLID hand and foot holds.
Either way, glad you made it back in one piece. For anyone who is contemplating doing this route, please keep in mind that this is one person's opinion. I'm not trivializing her opinion, but don't be deterred from a single person's experience. It's very doable without ropes as long as you're comfortable with the exposure.
