Very interesting, but I dunno.
Although with about the same meter, I can't convince myself that any similarity between "Red River Valley" and the Peacock-Flamman "We Will Walk in the Streets of the City" is more than coincidental. When sung, the two are different.

Can't find Taylor's or French's "Golden City." Also can't seem to find a New Orleans band version. I vaguely recall it, but it has been quite a few years since I heard it.

The chorus of "Come Thou Fount of Every Blessing" (not the Robinson- Nettleton version but the folk version in Brown, 562, p. 355 of vol. 5) has a suggestive meter*, but I can't convince myself that it is the same song as Red River Valley." Several tunes have been used for this hymn.

(*We will walk through the streets of the city
Where our friends have gone before;
We will sit on the banks of the river,
Where we meet to part no more).   

To date, no one seems to have found the 'ghost' song, "Bright Mohawk Valley" by Kerrigan. Its existence is doubtful, as noted before.