Looks like most of this advice is for the southern Sierra near Whitney, and it's all good advice in my opinion. But you're indicating you will be staying in the Mammoth Lakes area, which is a long drive away.
I think you've got a good plan for hanging out and sleeping at 8,000+ in style in Mammoth. There are great day hikes at higher elevation in that area. You mention the Mosquito Flat trailhead - which is an easy drive from Mammoth and puts you at 10,000+ ft to start. The day hikes up Little Lakes Valley are awesome and perfect for acclimating. You wrote "Mono Lake" but I think you meant Mono Pass, which is about 12K and a good day hike off that scenic valley of lakes.
So it would work well to stick with the Mammoth area first before moving down to the lower Owen's valley. Once you make that move, you should take the advice given above and camp as high as you can without sleep problems - the Portal is good logistically and socially. Cottonwood Pass/Horseshoe Meadows area is easy access to/from the Portal so it's a no brainer and a great area to explore with water, toilets, tables and walk-in campsites at 10K.
Have a great trip!
Here's a short video that includes an acclimation hike up Cottonwood Pass. We spent the night before in Mammoth and then we only had the one day to acclimate but we made it.
