I rode a tandem on the B-Line from Payson to the Roosevelt Lake turnoff in 2005 as part of the Greater AZ Bicycle Association ride across AZ. IIRC, there isn't much shoulder coming down to Rye but you don't need one because you'll be running close to the same speed as the cars. My experience may have been optimal being part of a large group so drivers were aware of cyclists on the road after passing the first dozen.

FWIW, I brake when brakes are needed; Not until then. I would worry about blowing a tire off it I wanted to chicken-brake all the way down.