Malcolm, thanks! Here is the version published in Pete Seeger's book, AMERICAN FAVORITE BALLADS (p.77):

The water is wide, I cannot get over,
And neither have I wings to fly.
Give me a boat that can carry two,
And both shall row, my love and I.

A ship there is and she sails the sea,
She's loaded deep as deep can be,
But not so deep as the love I'm in,
And I know not how I sink or swim.

I leaned my back up against some young oak,
Thinking he was a trusty tree.
But first he bended, and then he broke,
And thus did my false love to me.

I put my hand into some soft bush,
Thinking the sweetest flower to find,
I pricked my finger to the bone,
And left the sweetest flower alone.

Oh, love is handsome and love is fine,
Gay as a jewel when first it is new,
But love grows old, and waxes cold,
And fades away like summer dew.

(Repeat first verse)

No additional verse here. However, here is the additional verse (from some place on Google):

The seagulls wheel, they turn and dive,
The mountain stands beside the sea.
This world we know turns round and round,
And all for them - and you and me.

Traditional New Last Verse by Pete Seeger (1982)
© 1993 by Sanga Music, Inc.

I hadn't thought about Sharp's collection of English songs being published in this country so early - 1916! Of course it was available in print. So my question remains, did Sharp's collated version ever make it back into the oral tradition prior to the folk revival and was it ever collected as such? Or, did something like Mrs. Cox's version ever make it across the ocean to this country prior to the folk revival? If not, was Peggy Seeger the one who introduced it, presumably from Sharp's book(?) or from some other source?   

Since Sharp collected his unpublished verses of "Waly, Waly" from Jane Hicks Gentry of Hot Springs, I went to her book, JANE HICKS GENTRY, A SINGER AMONG SINGERS, by Betty N. Smith (University of Kentucky Press), and found it there. The date on it is September 14, 1916, which I assume is the date she sang it for Cecil Sharp. I says that it may also be found in Bronson vol. 3. The two verses are:

As I walked out one morning in May,
A-gathering flowers all so gay,
I gathered white and I gathered blue,
But little did I know what love can do.

Seven ships on the sea,
Heavy loaded as they can be,
Deep in love as I have been,
But little do I care if they sink or swim.

Malcolm, has the Sharp version that you have analyzed shown up in any of these threads? If not, could you perhaps post a copy of it? T.O.M.