Mudcat crashed while I was trying to post a message... trying again. A few more sources, most from the late 18th century:

https://archive.org/details/sim_weekly-entertainer-and-west-of-england-miscellany_1786-02-13_7_163?q=%22Hal+the+woodman%22
https://archive.org/details/bim_eighteenth-century_the-lyric-miscellany-or_1789/page/n3/mode/2up?q=%22Hal+the+woodman%22
https://archive.org/details/vocalmagazinecv11797ingl/page/96/mode/2up?q=%22Hal+the+woodman%22
https://en.wikisource.org/wiki/The_Woodman_(Linley)

One source gives the daughter's name as Madge instead of Kate.

The poem was written, as alluded above, by Thomas_Linley (1733-1795) some time at or before 1786

And my ignorance in ballads is showing: the Chevy Chase is obviously to Child 162, not Maryland...