One library, different Output styles

You just need to change the output style in the manuscript itself, not in the endnote program (which for the reasons you just described, never overrides the manuscript output style).  When you create a new manuscript, endnote “guesses” and applies an output style rather hit and miss. (that is-   I have never figured out how it picks one, sometimes it is the one you last used, sometimes it something out of the blue).  The output style can be changed from the endnote format bibliography tool or the endnote ribbon in Word.