We've done parts of this trip from both directions. If you start in Yosemite, I think it's better to start at Mono Meadows. You save a few miles, and some climbing, by doing that. But you have to pick up your permit, then drive the Glacier POint road. It's hard to get on the trail before about 11 a.m.
I think Lower Ottoway is a long stretch if you start that late. We camped along Illilouette Creek the first day, and then went to Lower Ottoway on the second day--one of our favorite places in the Sierra.
We also took the southern route, starting at Granite Creek trailhead out of Bass Lake, and hiking up to Isberg Pass, then back over Post Peak Pass. Wonderful stuff. We camped the first night at Sadler Lake, which is maybe 9 miles from the trailhead?
Either way you go, it will be stunning.
WE've got reports on both trips on our website: