Riding the Interstates in Arizona IS legal, unless it specifically states "no bicycles, mopeds", etc.
Have ridden parts of I-10, I-17 and I-19 many times. In places there is no other road options.
This ain't the eastcoast or the midwest; hell we can carry a non-concealed sidearm legally and without a permit. Try that one back east!
As for do-able, have cycled from the Grand Canyon to Nogales Mexico five times in 6 days via
Grand Canyon (south rim), Cameron, Flagstaff, Payson, Globe, Tucson, Nogales. Have done it on our tandem and on a single.
Have cycled the Flagstaf area and down Oak Creek Canyon into Sedona; very do-able.
There's about 6,000 feet elevation gain from Phoenix to the Grand Canyon.
Just have some decent gears and it can be done.