Don't know which is 'exacter' but the text printed in Fife and Fife (given first) differs from that rendered by Abby Sale only in grammar:
Doney-Dony; a-leavin'-a-leaving; blanket-blankets; a-grazin'-a-grazing; all round-all 'round; Oh, my feet's in my stirrup[!}-For my feet's in the stirrups.
'The feet's in my stirrup' (Fife and Fife) is a nice trick.
The only other difference is repetition of the 'Farewell' verse at the end. Your re-hearing may settle which is more correct.

Digression-
Of course we only have Morris's claim as to where he heard the song and the date.
There is Thorp's version, printed 1921, ("heard from a puncher who had been on a spree in Pecos City. He had taken a job temporarily as a sheep-rustler for an outfit..."
There is the version by John Lomax, printed in 1916 (not in the 1910 first printing); "sung at the end of a cowboy ball."

And I always liked the verse sung by Powder River Jack (1938):
Montana lies north and I'm ridin' all day,
Goin' to winter in the coulees where the badlands lay.
Old Paint, a good pony, he paces when he can,
He's up and a rearin' for we're bound fer Montan.'
Of course no one pays attention to his verses because he lied some-
like Lomax(?).
And the Ozark version found by Lucile Nelson (1929) reprinted in Randolph-
It's raining and it's hailing, the moon gives no light,
My horses can't travel this dark road tonight.
Go put up your horses and feed them on hay.
Come in and sit beside me, and talk while you stay.
My horses ain't hungry, they won't eat your hay,
I travel through Texas and feed on the way.
.......