Unfortunately, Dicho, my searches seem to be proving the truth of what you have said. However, here's a little song collected by Cecil Sharp from Mrs. Jane Gentry of Hot Springs, N.C. on September 15, 1916. There are some interesting overtones in verses 2 and 3 that perhaps share a context with "Limber Jim".

I whipped my horse till I cut the blood,
I whipped my horse till I cut the blood,
I whipped my horse till I cut the blood,
And then I made him trod the mud.

Refrain:
Coy ma lin dow, kill ko, kill ko,
Coy my lin dow, kill ko me.

I fed my horse in a poplar trough,
And there he caught the whooping cough.

I fed my horse in a silver spoon,
And then he kicked it over the moon.

My old horse is dead and gone,
But he left his jaw bones ploughing the corn.

[Cecil Sharp, ENGLISH FOLK SONGS FROM THE SOUTHERN APPALACHIANS, Vol. II, (1932), #219, p.311]

In 1950-55, Maude Karpeles, who assisted Cecil Sharp with his original collecting, went back to the Southern Appalachians to see if any of their original sources were still around. This time she took a tape recorder. She actually found a few of them and recorded them singing the same songs they sang for Sharp. And she found younger members of their families. These recordings are in the Library of Congress. They were also released commercially in Great Britain on two cassettes, by Folktracks. They are entitled: BLACK IS THE COLOR: ENGLISH FOLKSONGS FROM THE SOUTHERN APPALACHIANS RECORDED BY MAUD KARPELES 1950-1955 (Folktracks FSU-60-907) and CUMBERLAND GAP...(Folktracks FSU-60-908). On the BLACK IS THE COLOR cassette, Maud Long sings "I Whipped My Horse" (titled "I Fed My Horse", A8). She was the daughter of Jane Gentry. These cassettes are in the Library of Congress and are also possibly available through Interlibrary Loan from California. I could not find a source in Great Britain, but one should check at the Cecil Sharp House.