Route: Trans Yosemite (CA)

Ben Mitchell proposed this route crossing Yosemite National Park on the east-west axis:

The Trans-Yosemite Route: This route crosses Yosemite National Park laterally from Mono Lake to Hodgdon Meadows (east to west), or more exactly, from Mono Basin Visitor Center to Upper Carlon Day Use Area. 
If starting from Mono Lake (counter-intuitively, Mono Lake & Lee Vining are actually at higher altitude than Hodgdon Meadows), begin at the Mono Basin Visitor Center on Lee Vining Creek Tr. From here it's Hwy 395 to Tioga Rd/Hwy 120 to Vista Point Dr. Then you'll jump on a gravel/dirt rd before cutting the corner (to avoid a residence) to Horse Meadows Rd. Then take a hard left onto Aqueduct Rd, continue onto Forest Rd 1N17, and then onto Forest Rd 1N19 to Walker Lake. This is where the route turns to single-track. You'll soon connect with Bloody Canyon Tr, which makes a long, steep ascent to Mono Pass, just before entering Yosemite (amazing views). Once in the park you'll stay right for about 3.5 mi. Then you'll take a left on a little-used & hard to spot trail (not on most maps) that parallels Dana Fork to the PCT (joins with batter defined trail about half way). Go left on PCT, Left on JMT, & another right toward Vogelsang High Sierra Camp. Follow signs to Vogelsang HSC, to Merced Lake, and then Nevada Fall, Vernal Fall, & finally Yosemite Valley via the Mist Trail. The valley can be a bit confusing if you're not familiar. Follow the GPX route on your device (as is always recommended). After El Capitan Meadow, you'll connect with Old Big Oak Flat Rd, which you'll follow for the remaining ~20 miles (except for the last .6). Though for the most part a gradual climb, this is not as straight forward as it sounds. The first 4 miles or so consist of broken, intermittent asphalt, overgrowth, numerous rock slide zones, & one particularly challenging washout. Most are fairly easily navigable (watch for worn paths & cairns), but the washout zone is preceded by pretty bad overgrowth, and following the cairns and previous (& therefore expected) steady incline of the road grade will mislead you to an improvised trail in the side of a sheer rock face. To avoid this, when the thick overgrowth section begins, attempt to take a steeper angle uphill to follow approximately where the rd should have been (using GPS) in order to make it above the coming sheer rock face. (If you miss this & reach the washout, look uphill and you'll see some of the remaining rock retaining wall of the old rd.) After this ~4 mi section, you'll join with El Capitan Tr, a welcomed maintained section. Then it's Tamarack Flat Campground & a paved rd stretch to the Tioga Rd/Hwy 120 crossing. After another unmaintained section with some downhill, the old rd joins with Hwy 120 for a short bit. There's not much shoulder here and it is advised that you take the high ground, following deer trails when available, to reach Tuolumne Grove. Follow Old Big Oak Flat thru Tuolumne Grove and another 4 mi to Hodgdon Meadows. After joining with Tuolumne Grove Rd you'll take a right onto an unmarked rd (GPS) for a final .6 to Upper Carlon Day Use Area, just outside the national park boundary. There is a pit toilet and parking area here for 10 or so vehicles.
Please note that though the above route description is detailed, GPX data should always be used to more precisely follow routes.

CalTopo map: https://caltopo.com/m/DTGV

GPX file: https://drive.google.com/open?id=1-oNSTAVrz2vJ-Vzl70U32PCyiofsPsZL

AllTrails map: https://www.alltrails.com/explore/map/map-44228bc5-3fed-4fbf-938b-62641a91ddf8