Charley, I believe the idea that "A-Rovin'" is "one of the earliest shanties" is based entirely on Masefield's hasty conclusion, based on his observation that the theme and even some of the rhymes of Heywood's song are much the same as those of "A-Rovin'".

Otherwise, though, the songs are dissimilar.

Heywood:
http://books.google.com/books?id=BNUUAAAAQAAJ&pg=PA233&lpg=PA233&dq=%22feele+man%22&source=bl&ots=TSwGSRBj2J&sig=V5Y2fvB_OAXNr8mDhdARvW5TlhY&hl=en&ei=UnvoS_XTLsSblgf-7-WlAw&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCAQ6AEwAg#v=onepage&q=%22feele%20man%22&f=false

(Pp. 232-33).

What text of "A-Rovin'" did your family sing in the '40s?