Twin Peaks trailhead for ~2.6 miles to a wooden bench in the alpine where the doubletrack ends. From here, take the rough singletrack left and down to the creek. Cross the creek and either follow a rough trail along the creek to Twin Pass, or another faint trail with a more northerly trajectory towards the saddle east of East Twin Peak. Gain the ridge and head west towards East Twin Peak. At ~5000' the ridge will get more serious. Here the routefinding begins; it is beyond concise explanation. Pick your way around and through gendarmes and overly steep and exposed sections, at times on the north and other times on the south side, of the ridge. For the last few hundred feet to the summit, the north side offers gentler terrain. This route is more convoluted than the south gully, but with good route finding the climbing actually seems less intimidating. That said, pay close attention to your routefinding and don't get sucked into an overly dangerous spot!
This route is likely harder and more dangerous with snow; there is a lot of steep snow climbing with avalanche hazard along an exposed knife-edge ridge. Checkanchorageavalanchecenter.org
as a resource on snow conditions.