At the risk of looking like an idiot, I'll mention that the Mountaineer's Route is on the West face, about a 10 minute hike left from likely bivy locations. Seagull and Lost Horizons are directly above the bivy and start with a left leaning gully with chockstone topped by a triple tiered roof -- just like Mountaineer's Route. From the large number of bail anchors we found on these routes, others have made the same mistake while aiming for Mountaineer's Route.
If you do this one first your impression of climbs on the EP will be a little skewed. The route is on good but not great rock, and the rating is a bit soft. The other climbs that I did feature great rock and stiff ratings.