Your mention of tunes as 'something else entirely' touches a subject dear to my heart of late. And in JFSS and JEFDSS completing the songs from broadides is betterr that the many instances where they give tune and 1st verse and dismiss anything further by saying 'the words are on broadsides', because many of those broadside are now difficult to find. [Thank God for Steve Roud's indexes and Bodly Ballads website, as we can now find many of them.]
Tune bibliography is bit of a mess at present, and one reason I've been working on tune coding problems recently is to find a good way to code traditional song tunes so we can make a big file of reference data of tunes collected that will give us a basis for comparison of any other tune we might be interested in. We have many bibliographies of folk songs and broadside ballads now, but for tunes practically nothing. There are tune collections like C. M. Simpson's 'The British Broadside Ballad and Its Music', but the tunes there are not yet coded for ready identification. Cazden, et al, have a lot to say about relatives of the tunes in their 'Folk Songs of the Catskills', and Phillips Barry had a lot to say about tunes in the volumes of 'Bulletin of the Folk Song Society of The North East', and there are a few other editors that devote some space to discussion of tunes and relatives, and things go all the way to the other extreeme, where songs, but not tunes were collected, nor were the tunes even mentioned. [Alfred Williams 'Folk Songs of the Upper Thames].
Discussions about tunes that only give titles aren't very informative, since the same name gets used over and over for different tunes, and (what is only slightly different) the same songs was often sung to different tunes, and even when someone points out a tune in a specific work as the model, that's not very helpful if you can't readily find it.
Tune coding uses only the beginning of the tune to compare with the beginning of other tunes, to see if they are the same or nearly so, and can't prove identification of two tunes as the same, but it can screen out vast numbers that are pretty surely not related to a given tune, and greatly simplifies the identification problem.