...on my drives from Colorado to visit my mom in Saddlebrooke. I take Hwy 60 from Socorro, NM and drive through Showlow and the Salt River Canyon, so I go by these places. I just have not had the opportunity to check them out. Using Google Maps to browse the White mountains shows a few other places that look like you can paddle around and camp. None of these places look large.
The San Carlos Reservoir, while often low due to dry conditions, is a possibility. there are a few other high mountain lakes listed. Seneca Lake and Point of Pines sounds promising:
I know Roosevelt up above Phoenix is a madhouse - very busy.
Canoe Pack Liner
Full Size Sail Rig
Wabakimi Canoe Pack
Kayak Motor Kit