I've had my troubles with the search by keyword on the Bodley Ballads website, too. Yesterday I could find nothing under 'Benjamin', but today I get several listings, two being our ballad here. The copy designated BDN in my broadside ballad index is also in the Bodleian, in the Don collection, and that (and the one in the Crawford collection are the earliest.

Curiously, the late copy in the Douce collection is the only one that has the 16th verse (as the last).