The pink line on this photo goes all the way to the basin between the Horns and Goat Citadel. If, instead, you traverse the band of white aggregate, lower snow patch, and behind black prow (point below the "or" in "Little Horn") at 7500 ft along a reasonably well-defined goat path, you avoid the broad loose gully to the upper basin and the scree descent (ascent on the way back!) at the base of the Goat Citadel. You will come out at the saddle where the pink line intersects the larger black buttress. Your party will be mostly at the same elevation during this traverse, reducing the exposure to party-induced rockfall. The key to this route is following the white aggregate band, which is solid and easy climbing, to the promenent notch behind the black prow. From the black prow the view east to the black buttress across two major gulleys may look intimidating, but the goats have a nice path at the base of the cliffs, and the final 150 feet to the 7900 ft saddle behind the black buttress is on solid rock.
We attempted this route on the fly after our climb of Big Horn. We made it as far as Goat Citadel before we timed out. I'll be back for Gilbert.