Welcome ponation! I assume you have read the blog linked to in the AMS at 10,000 feet
thread, "JMT Thru Hike Derailed". That is about the worst case scenario you can get into. His experience is unusual, but it can happen.
I live not much more than 50 miles (but a 4+ hour drive) from Mt Whitney, at 300' elevation. I did a back pack last summer covering part of the JMT, and I'll share my experience. I was taking half a 125 mg Diamox twice a day.
Day 1: Drove to Horseshoe Meadows, slept the night in the car.
Day 2: Got a late start on my hike because I had to drive down to Lone Pine to pick up my permit (Sequoia won't let Inyo do an overnight drop box permit, so I had to stand in line and say Yes that I understood all the regs.
) I hiked to Cottonwood Lakes and camped at 11,600. I was tired but ok that night.
Day 3: Climbed Langley at 14k, then carried my pack cross country with a 2k gain and loss. Had to hike farther than planned due to not doing enough pre-hike research. I was exhausted at the end of the day. Barfed all my cookies before I went to bed. So much for the beauty of Sky Blue Lake. :-/
Day 4, 5, and 6 were ok, but I sure didn't have much appetite. I was hiking mostly off trail or on no-longer-maintained routes.
So... if you have the time to come in early and stay at Mammoth for several days, then another night at 10k, I think you will be adequately acclimatized. If you are more susceptible than most, this pre-hike preparation will help ensure that you will succeed on the JMT.