I've just double-checked Bronner: no mention at all of Gitz Rice.

Moreover, contrary to Carey, Richard Dorson did not say that "Gee, Mom" was ever sung to the tune of "The Old Chisholm Trail."

What he said was:

"The most representative [American military folksong] is known by its chorus, 'Gee mom, I want to go home.' Adopted by the Army, Navy, and Marines, this lugubrious plaint echoes such favorite ballads of the cowboys as 'The Old Chisholm Trail' and of the lumberjacks as 'The Shantyman's Life.'"

"Lugubrious?" Had Dorson never heard the song sung? It's wry satire, not a "plaint." Few GIs would seriously call upon "Mom" in front of their barracks mates.

He gives five stanzas (no tune) with ellipses to indicate lines omitted - no indication why:

                      "I Don't Like Navy Life"

They say that in the Navy
The biscuits are so fine
But one fell off the table
And killed a pal of mine.

CHORUS:

I don't like Navy life.
Gee, Mom, I want to go
Right back to Quantico,
Gee mom, I want to go home.

They say that in the Navy
The pay is very fine.
They give you fifty dollars
And take back forty-nine.

They say that in the Navy
The coffee is so fine.
It's good for cuts and bruises
and tastes like iodine.

They say that in the Navy
The chicken is so fine.
A leg dropped off the table
And started marking time,

. . . . .

They say that in the Navy
The clothes are mighty fine,
But I need Lana Turner
To fill out part of mine.

. . . . .

It would be unlikely for a sailor to wanna go "back to Quantico," which in WW2 was primarily a Marine Corps base. Possibly Dorson's source replaced "Marine Corps" with "Navy" and kept "Quantico" for the rhyme.

Another full WW2 text is in New York Folklore Quarterly in 1947, collected by Agnes Nolan Underwood from one or more of her students:

The coffee that they serve you
   They say is mighty fine;
It's good for cuts and bruises
   And it tastes like iodine.
I don't want no more of Navy chow,
Gee Ma, I wanna go home.

[Next comes the marching chicken, then:]

The spaghetti that they serve you
    They say is mighty fine;
Some rolled off the table
    and hung a friend of mine....

[The final stanza is about the doughnuts.]


If I can dig out the similar but less clever WW1 song from Dolph I'll post it tomorrow.

To repeat, it's quite a stretch, despite its popularity, to connect Gitz Rice's song with this one. It's like saying "Louie, Louie" came from "Meet Me in St. Louis, Louie." You can't deny the similarity.
;^)