This thread back from the dead........
I am perusing this area for a trip & see that the Topocoba Trail enters/exits Havasu Canyon via Lees Canyon (this USED to be the main trail to Supai village). Once on the rim it looks as if it's off-trail through sagebrush about 5 miles to Apache Point (although I suspect that there are at least game trails along this stretch.). At Apache Point one would drop down to the Esplanade (see Doug's notes here > (http://www.gloaming.com/rockgarden/GCRoutes/GCApachePointTrail.html
). Once on the Esplanade this route is cairned all the way to the South Bass intersection (+/- 18 miles) and is shown on most maps.
You may then head down the South Bass Trail and hike the Tonto east to Hermit, or detour down to Royal Arch and then east from Toltec picking up the Tonto @ Garnet and then over to Hermit.
I'd surmise that March would be best for this hike, with the best chance that the Esplanade would hold water in pockets on the Esplanade as well as through the Gems.