I have thru-hiked the route solo, and repeated many sections on shorter trips with friends.
A GPS is completely unnecessary. All you need is good map reading skills and adequate prep.
When I went solo, I carried a compass but never used it. If I did it again I would not even bring a compass.
I did however also carry a PLB. And was VERY glad about this decision. It provided piece of mind.
I would carry it again, and I highly recommend it. Don't become that guy we never hear from again.
My thru-hike was mid summer during a very low snow year. I did not carry an axe.
I agree that during early September you should not need it - unless we have a really deep year.
You will have no problem finding a place to pitch. I took a 5oz. solo tarp
without any trouble, and I did experience more than my share of weather.
However, if you are taking a sublite then you are probably taking trekking poles,
and I always say that poles really just get in the way on this route (if there is no snow).
Half the time you will be strapping them to your pack. To me that is too much weight for not enough use.
I resupplied only once, at Red's, after 6 days. I should have planned a 2nd re-up in Tuolumne, that was my mistake.
If you are going to take the whole month, you need one stop before Red's. Best choice I think is to go out over Bishop Pass.
On shoes...The trail runners are OK. I do a lot of that. Boots are certainly not mandatory.
However, I wear approach shoes for this kind of terrain.
With super sticky rubber, stiff soles, and toe armor, I have found that I am actually much faster
off-trail with approach shoes.
Lastly, if I had a whole month, in addition to your zeros, I would climb some stuff. Think about Sill, Feather, Ritter, Conness, and Matterhorn.
Best of luck!