The actual title of this song is READY FOR THE RIVER.

Here's the catalog description from Indiana University Sheet Music Collections:

Title: Ready for the river
Composer: Moret, Neil
Lyricist: Kahn, Gus, 1886-1941
Publisher: Villa Moret Inc.
Place of publication: San Francisco
Date of publication: 1928
Call Number: M1 .D48 Box: 026 Item: 057
Performance Medium: Piano and Voice (with lyrics)
First Line: Tell the world that I'm all thru with it,
Chorus First Line: Ready for the river, the shivery river,
Genre: Popular song
Subject term: Daniels, Charles N. (Neil Moret)

There is more to the song than what you quoted. What you call a verse is actually the chorus; in addition, there is at least one verse (see the version posted here) and possibly two (see the version posted in a blog).

But since you asked for my opinion... (Hey, I'm not used to this. I mostly post only facts, not opinions. I guess it's from feeling stomped on too many times by people who disagreed with my opinions.)

Your added chorus is excellent.

However, I think it would be a good idea to restore the original line "the river that runs down to the sea" and thus avoid having the line "so get that river ready for me" twice in each chorus.