Lucky Strike climbs up the middle of the South face of Gladstone on steep snow to the bottom of the upper headwall, then follows the right edge of the headwall on rock in a steep chimney to join the South ridge a couple of hundred feet below the summit.
The quickest way to gain the bottom of the South face is over the top of Cross Mountain (12,703'), climbed by its East ridge. Park at the Cross Mountain Trailhead a couple of miles south of Lizard Head Pass on HI145. Hike up the Cross Mountain Trail to its intersection with Lizard Head Trail for 1/2miles to "Lizard Head Pass" on the ridgeline between Lizard Head and Cross Mountain. Ascend Cross Mountain by its East ridge (3rd Class with a little 4th Class) and continue over the summit along the ridge towards Gladstone.
A short distance beyond the summit on the ridge is a wall that requires low fifth-class climbing. Backtrack 100ft and descend a steep scree gully west into the basin south of Gladstone. It is a straight-forward hike up the boulderfield to the base of the South face.
The South face of Gladstone is wildly complex, and like all of the Northern San Juan mountains the rock is loose and chossy. A prominent snow couloir extends out of the center of the face, which is the bottom of the route.
Climb the snow as it steepens and narrows straight up the middle of the face for five hundred feet. As you progress upward several rockbands are climbed through on steep water-ice. Rock protection can be had to the sides of the snow. About half-way up the lower half of the face a snow couloir exits the center chute to the right which allows easier access (AI3) to the South ridge of Gladstone and out of the face.
Above this exit climb through a low-fifth class rockband which angles up and left to maintain the line up the center of the face and regain the central snow couloir. This is where the terrain starts to get really steep and the last likely chance to rope up, if you have not done so already. The final stretch of alpine ice is sustained in its steepness and no ledges exist until forty or so feet up 5.7 rock above the couloir.
The crux: Once the bottom of the headwall is attained transition to vertical rock in a chimney on the right, which follows the right edge of the headwall. A chockstone blocks the chimney directly above the snow. A beautifully exposed handcrack on the wall right of the chimney allows access around the chockstone. Forty feet up the rock is a nice belay ledge which cuts across the bottom of the headwall.
Continue above the ledge on 5.7 rock and maintain a line which follows the right edge of the headwall. After 200ft the angle lessens and many ledges break up the terrain. Another 200ft of 5.5 rock brings you to the South ridge. Two to three hundred feet of fourth-class terrain gain the summit.
We started from Cross Mountain TH at 0230 on 9 June 2013, summited Cross Mountain at 0430, started climbing at 0730, summited at 1130, started descending the North Ridge at 1230 which we took into Navajo Basin (a bad idea based on afternoon snow conditions in Bilk Basin), and reached the truck at 9pm. We were only able to hitch a ride for about four miles of Dunton Road and HI145; proper prior planning prevents piss poor performance.
The North ridge of Gladstone is the standard route up and down the peak. It is rated Third Class. With warm afternoon spring snow all about we experienced steep fourth class terrain down the ridge-center (easier terrain exists just to the east around the upper difficulties, per this site) with what would seem to be low fifth class moves thrown in. It is narrow and exposed and loose. Do not climb below others, especially potentially less-aware hikers who may accidentally trundle a stone onto your dome.
Lucky Strike requires alpine ice to hold the rock and choss together in the lower half of the climb (perhaps it is a year-round route, though it would seem that spring is the best season). The best descent from the North ridge back to the Lizard Head Trail and Cross Mountain Trail to your truck is to descend to the east off of the ridgeline. If there is enough snow to climb, there will be lots of snow lingering in basin north of Gladstone, which will be very soft in the afternoon. Use extra caution descending into Bilk Basin east of the North ridge. Descend to Lizard Head Trail, climb south back up to "Lizard Head Pass" and descend the Cross Mountain Trail to the trailhead.
A cleaner but much longer route descends west off of the North ridge to Navajo Lake and the Navajo Lake Trailhead via the Navajo Lake Trail. If you choose this safer, longer route- park a shuttle vehicle at this trailhead, as the chances of hitching a ride on the Dunton Road(535) are based entirely on happenstance, and its a loooong walk to HI145, where it will still be difficult to get a ride. This descent route took us nine hours from the summit back to Cross Mountain Trailhead, and is not recommended less you park a vehicle at Navajo Lake TH. Even then it is a looong walk down.
A simple alpine rock rack should be sufficient, as the alpine ice is too shallow for pickets and the water ice through the several rockbands too thin for screws. Once it gets steep the rock quality drastically improves to take useful (more than psychological) gear. We carried only passive pro (tricams- the small and very large sizes, hexes and nuts). Cams could pry the blocks apart. A fall would still not be very clean and may pull the rocks out. Climb as if you are in a precarious place far from rescue, which is true. Bring a helmet, headlamp and the map. A mountaineering axe should be sufficient.
There is another description of this route on mountainproject.com. 13ers.com is also a good source of beta for the descent route down the North ridge.