The 367-80 was actually Model 707 and was given a spurious model number to confuse the competition.
No, the 367-80 wasn't the Model 707 but it led to two separate developments: the 707 (which bore only a superficial resemblance to the Dash 80) and the C-135 (which had more in common with its predecessor, such as the circular fuselage section, albeit wider).
The model 717 became the KC -135.
Also the C-135 Stratolifter.
Has anyone actually used the 717 name in the real world?
You mean like in the Type Certificate, for example ?