For what it is worth, we just bailed on our 12 day trip out of Cottonwood Lakes TH after 4 days ( we planned to acclimate for a couple of days at the lakes). The afternoon smoke was pretty bad at both Cottonwood and Southfork Lakes, so instead of going over New Army Pass we went back to the TH. We were getting ash fall on our tent in the afternoons. Mornings were beautiful, but the smoke would start to build around 11:00 am. The hike out was extremely smoky. Smoke in Lone Pine also varied but was thick on August 26 afternoon. We left Lone Pine yesterday morning, 8/27 and drove home.
We made a decision to leave the JMT in 2015 at Kearsarge Pass because of the Rough Fire and I never want to breathe in that kind of smoke again or take the risk of long term lung damage because of the small particulates. I had a horrible smokers cough for two months after that and I don't smoke cigarettes.
Obviously, the smoke varies depending upon wind direction, but the proximity of the SQF/Castle Fire is causing variable smoke conditions in the area. You may want to check out the link below from one of the admins of the JMT Facebook group that has links to websites with current smoke modeling and readings and make your decision. The Mt. Whitney Facebook group also has posts regarding current conditions and photos.
https://ingasadventures.com/backpackers-guide-to-tracking-california-wildfires/https://www.facebook.com/groups/30962451768I don't know the age of your Dad, but this kind of air is very dangerous for anyone with underlying heart disease. At our ages we think about those issues ( 68 and 73) :>)
Best of luck.