Okay here's a summary of what I found.
We start with the 1690 printing which has several copies but all the same printing house (Scarlet town-bound, 15v)

Then the mid 18thc reprints of this which are fairly numerous and carried on to about 1800 with the extra v on the end. Printed by the likes of the Diceys, White of Newcastle, and then Davenport c1800 (16v, again, Scarlet - bound)

Percy then publishes his slightly altered version c1765. The significant difference is changing 'bound' to 'born' in the first line, otherwise the differences between his and the Dicey copy are trivial. We have this version then by Fowler of Shaftesbury and some without imprint but 18thc (16v, Scarlet - born)

Then we get a longish rewrite some time in the 18thc that changes 'Scarlet' to 'Reading' a sort of reverse pun. My only copy of this is no imprint and mid 19thc unfortunately but I would say it seems to have given rise to both the Scots version and the later c1800 widely printed broadside. I will post this version later. (14v, Reading - born) This version is the only one to introduce the rose/briar motif)

Seemingly from this was made the Scots version which may first have appeared in a 1740 edition of Ramsey. It lacks the first verse. ( 9v)

Then we have the widely printed 19thc version which seems to appear c1800 with Pitts, Swindells, Kendrew followed by all the usual suspects like Catnach and all the Pitts/Catnach successors. (10v, Reading - born)

The Philadelphia Forget me not Songster c1842/3 version is the Scots version filled out with all sorts of commonplaces and repeats very much in the Peter Buchan style. (18v)