While watching Ken Burns' The Roosevelts I noticed that from the days of TR up through the early 1960s, footage of the party conventions where presidential candidates were nominated seemed to prominently feature the delegations from the Canal Zone. Nothing specific was mentioned about this, it was just a visual detail that I happened to notice and found intriguing.
While the Canal Zone is no longer a US territory, this article from PRI suggests that Guam, the Virgin Islands, the Northern Mariana Islands, American Samoa, and Puerto Rico all vote in primary elections, despite their lack of representation in the Electoral College.
There was quite a bit of news coverage back in March when Bloomberg won in American Somoa, which will apparently have 6 delegates to the Democratic Convention.
All of this has me wondering if there was any specific election where the delegates of such territories have had any significant influence. Was there a close call where their votes were decisive? If not, have the delegates ever had any other kind of indirect influence, like a prominent speech or some kind of activism on the convention floor?