Connections to "The Lone Star Trail" (in the DT) could be coincidental. The protagonist here is a committed cowboy who periodically leaves his girl and drives cattle to Kansas, where he may go on a bender. The verses in question are:

I went up the Lone Star Trail in Eighteen Eighty-three;
I fell in love with a pretty miss and she in love with me.
"When you get to Kansas, write and let me know;
And if you get in trouble, your bail I'll come and go." (Yell)

When I got up in Kansas, I had a pleasant dream;
I dreamed I was down on Trinity, down on that pleasant stream;
I dreamt my true love right beside me, she come to go my bail;
I woke up broken-hearted with a yearling by the tail. (yell)

The version of "Root, Hog or Die," in the old edition of Cowboy Songs, is definitely related to "Logan County Courthouse." The story is similar but the locale is changed. The protagonist had "a white hat, a horse and buggy fine, Courted a pretty girl and called her mine, etc." The song was omitted from the 1938 edition of Cowboy Songs.