"Neptune's Raging Fury," from the Bodleian broadside, is printed in Christopher Stone, 1906, "Sea Songs and Ballads," Oxford University Press. In the notes, Stone remarks that it is altered from Martin Parker's original song, ca. 1635.
Stone says it also appears in Roxburghe Ballads (Ballad Society), VI 431ff.
Also in Stone's collection is "The Bay of Biscay O!" by Andrew Cherry.

Lyr. Add: THE BAY OF BISCAY O!
Andrew Cherry

Loud roared the dreadful thunder,
The rain a deluge show'rs;
The clouds were rent asunder
By lightning's vivid pow'rs!
The night both drear and dark;
Our poor deluded bark!
Till next day,
There she lay,
In the Bay of Biscay O!
2.
Now, dash's upon the billow,
Her op'ning timbers creak:
Each fears a wat'ry pillow!
None stop the dreadful leak!-
To cling to slipp'ry shrouds
Each breathless seaman tries,
As she lay,
Till the day,
In the Bay of Biscay O!
3.
At length the wish'd-for morrow
Broke through the hazy sky;
Absorb'd in silent sorrow,
Each heav'd a bitter sigh!-
The dismal wreck to view
Struck horror to the crew,
As she lay,
On that day,
In the Bay of Biscay O!
4.
Her yielding timbers sever;
Her pitchy seams are rent!
When Heav'n (all bounteous ever)
Its boundless mercy sent!
A sail in sight appears!
We hail her with three cheers!
Now we sail
With the gale
From the Bay of Biscay O!

Christopher Stone, 1906, "Sea Songs and Ballads," XX, pp. 32-33.

Notes, p. 200, by Admiral Sir Cyprian Bridge, G. C. B., who remarked, "Introduced to the forecastle from the shore and rather a favorite, most likely because of its rousing chorus."