The DT has the version of "I Saw Three Ships" usually sung, apparently close to the text from "Christmas Carols, Ancient and Modern," ed. Wm. Sandys (London) 1833. The last verse in Sandys has "Then let us all rejoice amain," rather than "Then let us all rejoice and sing,..."

The original dates to 1666, in John Forbes Cantus, 2nd ed.
The Forum is dead, and I can't find anything via the filter.

Versions in the Bodleian Library have a first verse that begins "As I Sat..." I posted one of these in thread 54556 ("The Sunny Bank," ca. 1821-1827): Christmas failures

The Oxford Book of Ballads, ed. Arthur Quiller-Couch, 1910, has one beginning "As I sat...," as no. 104.
What was the 1666 version? Is it closer to the "As I sat..." versions?
Here is the Quiller-Couch entry.

I SAW THREE SHIPS

As I sat under a sycamore tree,
-A sycamore tree, a sycamore tree,
I looked out upon the sea
On Christ's Sunday at morn.

I saw three ships a-sailing there,
-A-sailing there, a-sailing there,
Jesu, Mary and Joseph they bare
On Christ's Sunday at morn.

Joseph did whistle and Mary did sing,
-Mary did sing, Mary did sing,
And all the bells on earth did ring
For joy our Lord was born.

O they sail'd in to Bethlehem!
-To Bethlehem, to Bethlehem;
Saint Michael was the sterésman,
Saint John safe in the horn.

And all the bells on earth did ring,
-on earth did ring, on earth did ring
Welcome be thou Heaven's King
On Christ's Sunday at morn!
(horn = prow; bare = old form of bore)