Maybe gringo is just onomatopoeia, i.e. not based on any one particular word or phrase, but just an attempt to evoke the generally more guttural sound of English and other Germanic languages in contrast to Spanish.

I was taught that the Greek word for foreigner, βάÏ쳌βαÏ쳌ος (whence barbarian), originated in that way, as a representation of how foreigners from the north sounded to the Hellenes.