I've hiked almost all of the Tonto in various parts. A thru-hike would be a very cool project, though the drive out to the South Bass TH is long and slow. I imagine you could find a company to do that shuttle, and I imagine it would not be cheap.
Easier logistically would be going from the Hermit or Boucher to Grandview or New Hance. Going down New Hance and up Hermit would probably be my choice, and you could easily spend a week on such a route.
Beware, the quality of the trail and ease of walking varies quite a lot. The stretch between the Bright Angel and Hermit is very nice and by Grand Canyon standards pretty easy. Other parts, such as Grapevine and Cremation canyons, are much harder than they look on paper (and descending New Hance is tough, to say nothing of going up it). Add to that variable water sources and the fact that September can still be very hot and you'd have a potentially character building trip. In a good way, of course.