I am still trying to figure out how you hike Mt. Whitney alone during Whitney Prime Time...the 4th until the end of September.
You may be hiking by yourself but you will not be hiking alone. With that said, you have to be disciplined and you have to all required stuff in your pack and know how to use it.
At home...you write a detailed itinerary, Re Conn Trip Record is the best prepared form for this.
On the trail...You follow your itinerary, you do not do a side trip to Mt. Muir, if it is not on your itinerary. If you start to feel the effects of AMS you turn around. If for any reason you don't feel right about things, you turn around. All this requires discipline. I would also suggest you be below Lone Pine Lake before darkness.
I have hiked Horseshoe Meadows to Whitney Portal solo but I did not do it a alone, there were loads of people on this route every day I was out. Think of Mt. Whitney as the Ski Hut Trail at Mt. Baldy only higher and longer. There will be tons of people with you on the way up, not so much on the way down...kind of like Mt. Baldy.