Kane states in the Approach section of his Ice Mt, NE Ridge route description that he does not remember seeing any cabins at Hamilton and assumes it is the site or place where a once booming mining town stood. On my last trip there in July, 1999, the foundation of an old cabin was visible across the creek at the site. I will post photo of it to the peak description.
I've hiked up into Apostle Basin once in winter and once in summer (yesterday) and was extremely confused both times by the route description. I don't think there is a spur trail, and I don't believe it's necessary to turn off the Apostle Basin trail. Following the Apostle Basin trail will take you along the route described.
Awe Yes....Almost a decade ago there was always a lot of confusion about this approach, and there still seems to be questions. I remember when I wrote up my description thinking there are going to be mountains out there that logistically will always challenge. With Ice, I'm not sure it's a bad thing that people get confused with the approach. I'm guessing the confusing approach has kept a lot inexperienced hikers away from the peak. Those that really want Ice will have to work for it..like you and me. Anyways, here is a link to my submitted topo from back then. Does this map look pretty good to you bases on your experience?