Unfortunately, in Yosemite, you are more likley to encounter backcountry rangers then anywhere else in the Sierras. And Little Yosemite Valley (and Merced Lake) are 2 of the most likley places to encounter one. When you get out of the Yosemite Valley to Tuolumne Mdws corrider, you are far less likely to see one.
Since you already have a permit, you just need to get them to modify your existing permit which is easier then applying for a new permit since you already have the starting trailhead reservation. This should be easy since you have the campsite most people request(Little Yosemite Valley) so taking a less desirable campsite further on shouldn’t be an issue with the ranger at the wilderness permit office. I personally, would keep your existing permit and spend half the day on top of Half Dome and call it your adapting to high altitude day.
Miner