Another SPer and I did the route on August 9 of 2008 and while it wasn't in mixed conditions, it was later in the year than I would recommend. There was some thin ice and snow cover in spots, but the bigger concern is that because of the low snow level the rock on the edges of the gully wasn't the normal "decent" rock where some of the fixed gear is. I couldn't reach the fixed pins en route, and the rock gear we placed was in the most rotten rock I've ever tried to protect.
I'd recommend a bit earlier, depending on the heat of the summer of course. I'd take a few screws (4-5 I would think), and then a smattering of rock gear. I only placed 2 screws I think...it was still mostly a snow climb, even with the near-meltout.
I'd personally recommend camping below the Lower Saddle. I've spent a few nights there and it always seemed nicer to stay a bit lower, at the Moraine or Caves. But I can't speak from experience, and the day is a bit shorter starting from the Lower Saddle. It's a trade-off.
I've never done any of the other gully climbs, but if it were me and I wanted to step up a notch, I'd look at the Enclosure Couloir.