This is a significantly longer hike than the hike from Clear Lake, but it can be done without a 4WD, and it is through nice territory.
To Island Lake
Take The dirt road #585 off of Route 550, 2.2 miles North of Silverton to the South MIneral Campground, at ~9,800 feet. Walk about two miles up the trail till you enter the Lower Ice Lakes Basin, at about 11,600 feet. From here, you have some choice about how to get to Island Lake. You can look for a faint path that is reported to leave from near the bottom of the Lower Ice Lakes Basin, you can do what I did, and just head straight up to the right, and It was fairly easy to find a class 2 way up through the rocks. Or you can go up to Ice Lake and look for a trail that goes from Ice Lake to Island Lake, around the prominent ridge that separates them.
From Island Lake to the Top
From Island Lake, look right, up towards Peak 13,309 (your objective), come down the ridge to the left (towards U. S. Grant Peak a little, and look down towards you for where the snowbank funnels through some cliffs near the bottom of the slope. Climb up towards this, go through the cliffs, a great place, and head up snow slope to the ridge. Keep to the left for slightly less steep snow, but none of it is particularly steep. When I went in late June of 2005, a snowy year, the scree was just beginning to show up at the top, but it was rather nasty unstable scree, and I'm glad the snow was there for the steeper part. then when you hit the ridge, simply stroll up the ridge (a couple of very insignificant class 1 or maybe 2 obstacles), to the top. The snow makes for a great descent route.
You want to bring an ice axe for sure, crampons depend on the conditions, in late spring on a warm day, I didn't miss them at all. I wouldn't think there was a reason this couldn't be done in the scree, but it would be a very steep loose slog. It was all snow, no ice, so it just depends on the snow conditions. You can treat water at Island Lake, around 12,400 feet, and in numerous streams by the trail up to the Lower Ice Lakes Basin, so if you have a water purifyer, you won't need to carry very much water at all. A rain jacket of some sort would be good, especially as the summer progresses into the apocalyptic thunderstorm season.
If anyone has better information on trails to Island Lake, I would love to have it.