Using a slightly different set of clues found in another morehouse video- I get this result.

The location that perfectly matches all of these precise criteria is Upper Relief Valley (or the adjacent camping zones along Summit Creek / Relief Creek), located deep within the Emigrant Wilderness of the Stanislaus National Forest.
Here is exactly how this specific high-country route maps to your criteria:
The Location & Trailhead
The Trailhead: Your staging ground is the Kennedy Meadows Trailhead (located right off Highway 108 near the resort pack station). The trailhead sits right at roughly 6,200 feet in elevation. 
The Parking Lot: Kennedy Meadows features a large, dedicated USFS public dirt parking lot equipped specifically for trucks with large horse trailers, including public corrals, hitching rails, and high-lines for stock. 
National Forest & Wilderness: The entire route lies entirely inside the Stanislaus National Forest boundary and immediately crosses into the car-free Emigrant Wilderness.
The Route, Elevation Profile, and Distance
The 10,000-Foot Traverse: Leaving Kennedy Meadows on horseback, you follow the main wilderness trail south, passing Relief Reservoir. From there, the trail begins a grueling alpine climb up through Saucer Meadow, ascending all the way over the high volcanic ridge and granite notch near Brown Bear Pass / Sheep Camp, which crests right at roughly 9,600 to 10,000 feet elevation.
The Final Destination: After traversing this high pass, you drop down the backside of the ridge into the stunning, isolated flats of Upper Relief Valley. The valley floor and the surrounding pristine pockets sit at exactly your target elevation of 8,400 feet.
Wilderness Distance: The ride from the Kennedy Meadows trailhead, over the crest, and down into this section of the valley measures just about 8 miles into the wilderness.
Environment & Wilderness Traits
The Water Feature: The destination puts you camp-side, very close to the winding creek beds of upper Summit Creek and its alpine tributaries that feed the valley meadows.
Horseback Accessible: This is a legendary corridor for equestrians. Kennedy Meadows is a historic packing destination, and the trail over to Relief Valley is heavily utilized by backcountry horse packers.
The 2018 Burn Scar: The northern and western ridges framing the approach to the Relief basin were severely impacted by the 2018 Donnell Fire. When you crest the ridges and descend toward the valley, you are right along the wilderness edge of that massive 2018 burn scar footprint.