The Kulshan Cabin no longer exists, it should say former site and mention that it just looks like campsites. You don't simply take a right onto the Hogsback moraine, you take the right fork of the trail that reads "climbers trail" (other fork goes to coleman glacier overlook) which then takes you to the hogsback moraine. You head straight up the tongue of the glacier around the left of a rock outrcrop ascending 1,200ft to bellow the black buttes (est. time: 1-2hrs). You head right towards the end of the roman wall, crossing a bergshrund in late season, and your there. It's a good idea to be roped up ALL THE TIME on this route, especially in late season. Est. Time from basecamp to summit: 4-7hrs.
Other than that awesome job, I posted a picture with a route line on it.
I'll be the first to admit it, but I'm sure I'm not alone- at 4750 ft there's a pretty good wash that you scramble over, and my dumb ass went up it for a few minutes before deciding that I was wrong. Cross that at roughly the same level, and you'll be ok. Also, I missed the sign that Duseks mentioned about the "Climber's Trail" (it was dark), but for those who miss it, the right turn to the Hogsback moraine is behind a couple of trees right at 5,000 ft.
There is some confusion about where the Roman wall actually is. Some maps (e.g., Green Trails Mt Baker map WA 13) show it as the rock ridge going S from the summit plateau. Other maps (such as the Terraserver map http://terraserver-usa.com/usgsentry.aspx?T=2&S=11&Z=10&X=1465&Y=13508&W=3&qs=%7cconcrete%7cwashington%7c) and the Beckey guide show it as the top of the rock immediately to the W of the summit plateau. Hence the confusion on this page as well.