Jer made this up after our trip over Crossover Pass two weeks ago.
The first chance for water would be the snow-slopes leading down from the initial notch where you leave the Slesse Creek descent ("Critical Routefinding 1"). These face North, and although we easily avoided the snow, I think it'd be a pretty rare year when there wasn't some left.
It was pretty slimy as we dropped down from the "Wooded Stump" to the "Orange Scree"; if you were hard up, you could squeeze some water from the scunge...
We had camped (en route to the N Rib) roughly where the "Orange Scree" meets the sub-alpine, and had no problems finding (slowly) flowing water there. I imagine those little streams flow all season.