Full trip report on my website: https://sites.google.com/stephabegg.com/colorado/tripreports/lafreeway2
A note on why we ended up "supported": We set out planning on an "unsupported" female FKT, having done no advance water-stashing and planning no external support. However, we discovered the exit moves for the Cables Route (5.4) on Longs Peak to be quite iced up. While debating retreat and approaching the summit via the Keyhole Route, a party arrived at the rappels at the top of the route just above us. I (Steph) happened to know one of the members of the party, and we ended up having a rope thrown down that would help make the iced up exit moves non-fatal. So, because of this 5-foot roped-up section using the assistance and gear external to our team, we put ourselves in the "supported" category.