Having done the whole JMT, let me say that it is far easier to end your hike going DOWN that big hill from Cathderal Pass west of Tuolumne Mdws to Happy Isle rather than to start your hike with it.
Cathederal Pass is 9,700'
Yosemite Valley is 4,035'
That is 5,665 feet of elevation change in 16.7 miles
The only truly level spot in that is Little Yosemite Valley.
Which direction would YOU rather go?
Be sure your permit allows you to stop overnight at Little Yosemite Valley campground. Enjoy a great swim in the Merced River. Note there is a ranger station at LYV and they WILL check your for bear can and your permit, which needs a special endorsement to camp at LYV.
Leave your car in the parking lot at Mammoth Mountain Resort. Take the shuttle bus down to Reds Mdw Resort and head for the valley.
From the Valley, take the 5:30 pm YARTS bus back to your car. Be sure to make reservations for that bus or get in line very early; it is the main transport for workers between the Valley resorts and their homes in Mammoth Lakes.