John
As I said, the link doesn't have to be direct from the Reliques. The material was copied into many other books and possibly was a source for some broadsides.

From the surviving evidence I'd say the songsters like The American Songster/Forget-me-not, and Western Songsters were more of an influence c1830-40 than the broadsides. Apart from printers like Coverley and Deeming I haven't seen a lot of evidence of American single sheets or garlands from this period.

From what I remember Bruce's site was more to do with the early history of traditional stuff on broadsides, 16th 17th centuries, but as that's what I'm interested in I might just have been looking at the wrong bits. I think there is a list of Child ballad references on the site, but it takes a bit of navigating.