Hey Joe, check out the forests just north of Mammoth on either side of 395 as you climb up the local summit. There are dirt roads on both sides with great choices for dispersed camping, some leading to seasonal creeks. 4WD recommended for best options. Can be heavy OHV use in the general area, but not a bad trade off.
Tioga Road, I would avoid that specific road for dispersed camping due to Yosemite traffic, but there are plenty of other roads to explore in the general vicinity. The east side of 395 has lots of FS and BLM land south of Mono Lake, and you can get into forest if you climb up into the hills.
For acclimation purposes, we often spend a night at a spot off Virginia Lakes Rd (~10K ft). There's dispersed camping, some primitive official spots, and a campground that might have a spot open. Also check out Lundy canyon campground and similar trailhead roads heading up into the mountains, just not Tioga Rd.
