I travel these roads often with my 5'er with no troubles.
I'd check the weather, (including the previous 24-36 hours).
If clear, take the roads thru Holbrook, Heber, and Payson (377-277-260-87) and you will be fine.
The I-40 to I-17 route is a safe alternate in case of bad weather, but is much longer, and no fun on a Sunday afternoon/evening due to returning weekenders.
2010 Dodge Ram 2500 Big Horn 4x4
2011 Jayco Eagle Super Lite 30.5RLS