The 1882 Indiana lines I posted in Oct 2018 appeared a little earlier in the Indianapolis Journal in 1880.

The title of the orginal is given as "Bill Crowder and Davy Crockett":

We fought half a day, and then agreed to stop it,
For I was badly licked, and so was Davy Crockett;
When we came to hunt our heads, we found 'em both missin',
For he'd bit off mine, and I'd swallowed his'n.