Robbie,
Perhaps you could explain in what way, shape or form Billy Boy can be related to any versions of Lord Randal. Without looking in great depth I have a 1776 printed version of Billy Boy called 'My Son Johnny O' in 12 stanzas. All 12 stanzas, just like the many oral versions, simply involve a mother asking questions about her son's new bride and the lad's answers, no poisoning, in fact the only negative is she's not fit to go to the well but he can do that anyway.

As for 'Ilkley Moor' being related, well that's surely cloud-cuckoo land!