The Penguin text was a collation; partly from the traditional sources named, partly from a broadside, and with some touches from Cecil Sharp's redaction and a fair few from Bert Lloyd himself. The "backdoors" line appears in most sets found in oral currency (including the Copper Family version), as on the broadside from which they all seem to derive: Lloyd replaced it with a poetic flourish that was, so far as I can tell, entirely of his own invention.

For more background, see thread  Penguin: The Ship In Distress.

The set printed by Roy Palmer is copied in DT file  SHIP IN DISTRESS. Unfortunately, the source is not credited: the tune was noted by George Butterworth from Mr H Akhurst at Lower Beeding, Sussex, June 1907; while the text was, according to Butterworth, "noted in Shropshire" (Journal of the Folk-Song Society, IV (17) 1913, 320-321; he gave no further details).

Penguin is now available in a revised and expanded form, as Classic English Folk Songs. It can be ordered from the publishers, The English Folk Dance and Song Society.

There is also a small suite of web pages providing additional materials; these include what I think is the only full transcription of the broadside available anywhere online:

Classic English Folk Songs: Supplementary Material.

A few small details of your transcription are probably mis-hearings; other changes are presumably down to Martin's memory. I'll know when I hear the recording.