I had intended to post a list of links last time there was a discussion of this song, but evidently didn't get around to it. Here, then:

In the Forum:

Info Req: Polly's Love  Text as found by Jim Eldon in Yorkshire, and recorded by Waterson-Carthy.
Lyr Req: Pretty Polly / lost verse  Two unattributed texts, presumably American.

In the DT:

THE CRUEL SHIP'S CARPENTER  Described as "transcribed from the singing of Mike Waterson"; with tune.
PRETTY POLLY (2)  From Dock Boggs, with tune.
THE SHIP'S CARPENTER  from Leo Spoencer, Canada, 1962. With tune.

There are two main entries at  The Traditional Ballad Index

Cruel Ship's Carpenter, The (The Gosport Tragedy; Pretty Polly) [Laws P36A/B]
Pretty Polly (II) [cf. Laws P36]

Several examples can be seen, and heard, at the  Max Hunter Folk Song Collection

Pretty Polly Come Go Along With Me  As sung by Ollie Gilbert, Mountain View, Arkansas on June 25, 1969.
Pretty Polly  As sung by Sara Jo Bell, Harrison, Arkansas on August 25, 1969 .
Pretty Polly  As sung by Harrison Burnett, Fayetteville, Arkansas on August 18, 1960.
Molly Girl  As sung by Mrs. Ed Newton, Gainesville, Missouri on June 10, 1958.

At  Bodleian Library Broadside Ballads:

The Gosport Tragedy or, The Perjured Ship-Carpenter  No date. Printed and Sold at the Printing Office in Stonecutter Street, Fleet Market .
The Gosport Tragedy or, The Perjured Ship Carpenter.  Printed between 1797 and 1846 by J. Turner, High Street, Coventry.

There are several 19th century broadside examples of the later version; they vary very little. Here is one:

Polly's love, or The cruel ship carpenter.  Printed between 1819 and 1844 by J. Pitts, Toy & Marble Warehouse 6, Great St.. Andrew Street, Seven Dials, London.

These are large images.