Since there was slavery in the Americas between their discovery and 1856, do we know of any Jewish slave-owners there who observed slavery-related laws of Judaism?
From a conversation with Eli Faber (A professor of history at John Jay College in New York and author of Jews, Slaves and the Slave Trade: Setting the Record Straight):
Based on his extensive research into the matter, I think we can conclude that this was the extent that Jewish slave owners observed slave-related commandments in the Americas.
Slavery related laws that I'm aware of, refer to Jewish slaves.
There are two types of slavery regarding Jewish slaves. One is when one kidnaps a person and enslaves him. I just happened to read in this week's parsha Ki Seitzei 24:7 "If a man is found kidnaping a person of his brethren among the children of Israel, and he enslaves him and sells him, that kidnaper shall die, and you shall remove the evil from your midst."
The other is in Parshat Mishpatim when a man is in debt and pays off the debt through slavery. That is where all the slavery laws I know of are listed. Regarding how to treat him, how and when to release him etc. Does not have relevance to slavery in Americas.