I climbed Mount Stuart a year ago this weekend via the south side, the Cascadian Couloir. I also live part time in the Teanaway valley. Although this year has produced a very wet spring with a lot of late snow, last year the couloir was almost all melted out so I dont know how much snow will be left. From the Esmeralda trailhead, go up the trail to Longs Pass, then drop down the bowl to Ingalls Creek trail. From there head downstream for a quarter mile or so until you find the climbing trail take off to the left.
On another note, have you looked at any of the avalanche warnings for this weekend? You really should check out the report from the NWAC for this weekend, it doesn't look very promising. With the recent snow we've gotten and the forecast for really warm weather this weekend, it is gearing up for some bad avalanches. In fact, with this report I wouldn't even consider being in that couloir... it would be an avalanche death trap. In most places the chute is deep enough that it would be extremely difficult to get to a safe spot in the event of an avalanche. I would seriously reconsider going up there this weekend, try finding some rock to climb or something.
If you have any more questions about the area or the forecast, just message me and i'll try to help.
Chase