I put a reference to this discussion on Fiddle Hangout, which seems to be composed largely of American 'Old Time' fiddlers - but no one there is familiar with a tune of that name. Some tangential stuff related to (possible) meanings and uses of "black rack".

Here's a couple of comments that may cover material you are already familiar with:

- In the context of Brer Rabbit stories, "rack-back-Davy" refers to a specific dance, or jig.

In one story, Miss Meadows is holding a dance and is counting on Brer Coon to perform the "rack-back-Davy" while Brer Bear demonstrates the "roasting-ear shuffle".

- The book...The Refugees: A Sequel to "Uncle Tom's Cabin."
Annie Jefferson Holland · 1892 references Rack Back Davy as with other fiddle tunes...

"Rack back Davy , " " Fisher's Hornpipe , " and the " Devil's Dream . " The Colonel grew jolly , and declared he would set up all night to listen to such music . The young folks formed a set , and dancing was kept up till the " wee sma ..."

https://www.fiddlehangout.com/topic/60244/#608771