Steve,
Is the text of "Paddy's Ramble (to London)" available online? It'd be interesting for me to see which verses in field recorded texts descended from it.

Teague's Ramble can be seen here:
https://mudcat.org/olson/SONGTXT1.html#TEGRMBL

The American "The Old Gray Mare" broadsides I've seen look like they were taken from existing traditional versions, they're lacking verses and expressions found in some of the field recorded texts such as the "I pulled my head off, the majest' to greet" from Charles Ingenthron in Missouri. And the Canadian texts make no mention of Nottingham and have some unique verses of their own.

Do you think they all go back to "Paddy's Ramble"? Could there be another British broadside that mentions Nottingham? At least it'd make sense to me since so many US texts mention Nottingham. This is me assuming "Paddy's Ramble" is set entirely in London without having seen the text.

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A detail worth mentioning (I forgot) above is that Beckham Ritchie in Carrie, Kentucky, in 1962 introduced Fair Nottalin Town by saying:

"If a man would make a song with never a word of truth in it they would free him, he was sentenced to die."

It further connects the Ritchie family version with the one Senator H. H. Smith sung in Knott County, Kentucky, about 1910. It seems there was a common tradition of prefacing the song with this story.

I also forgot to mention above that Vance Randolph recorded Charles W. Ingenthron at Walnut Shade, Taney, Missouri in September 1941. That's when he sang Nottingham Fair as it appears on the 1947 LP "Anglo-American Songs and Ballads" The Library Of Congress - AAFS L20.

Try as I might, sometimes I forget things or make mistakes and don't notice it until after posting.