Autograph Letter Signed, Pittsfield, Massachusetts, 29 October 1858.

So Herman Melville and the author of Kaloolah did meet, one time. Melville said so in a letter to Anthony Bowman of Boston, dated October 29, 1858:

"I never had the pleasure of meeting Dr. Mayo but once--now several years ago."

Melville, Herman (1819-1891) Autograph Letter Signed, Pittsfield, Massachusetts, 29 October 1858.: View auction on www.skinnerinc.com

We're short and way too late for this one: sold on May 27, 2015 for $20,910.