Child Ballads as opposed to broadside ballads (I know a lot of the Child Ballads appeared on broadsides)should be easier to study and come up with some general conclusions, which is one reason why Richie's collection may prove valuable. What I'm proposing can only be useful in very general terms and can't be actual proof, but if multiple US versions of a ballad differ significantly from their British counterparts it shows they have been in oral tradition in America for a significant period of time. The more and varied the differences the longer they are likely to have been in oral tradition there. An extra factor that would need adding in is the interference of broadside and literary versions, and indeed forgeries. Literary and forged versions can easily and quickly slip into oral tradition. I base my theories on my studies of broadside ballads over a long period. Those, generally speaking, that vary the most are the earlier ones like The Gosport Tragedy. What must be factored in here of course is the influence of intermediate printed texts.

You mention Bronson. I can't imagine Bronson being any use here as of course he was only dealing with texts with tunes and as far as I know, prior to Sharp there weren't any American collections that gave tunes, although Child himself may have had some.