Your most important task is to get the entry permit from the TH you want when you want.
The rest will come - by hell or high water. Once you're actually *in the mountains* with a valid entry permit, then it's much more flexible. That is, rangers aren't up there to force people to stay in the mountains if they aren't feeling well, have an injury, etc. There's multiple exit routes, including the MMWT, to get out of the back country.
Secondly, if you really want some assurance, then simply reserve an exit at Cottonwood. If for some reason you cannot make a permit change and get a walk-in MW exit, then take an extra day of food or so and just hike another day or two to Cottonwood. If you don't have the time/desire to hike to Cottonwood from Bishop (S Lake), then change the entry further south to Kearsarge with an exit to Cottonwood.
Any section of the JMT/PCT is world class, so it's easy to mix/match around specific targets. In this case, Whitney. I get that you're stressing, but I'm trying to assure you that it all shakes out in the end. The number of people who flake/bail for whatever reasons on any given day is around 50% by my guess.
Steve has stats that show the number of walk-ins for *lottery* reservations that become available once lapsed. Day to day, it seems to average around 50%. The only dates I recall seeing every permit picked up was like the 4th of July in a low snow year.