I am writing a novel that takes place in Galveston during the 1900 hurricane. I found an amazing book called The Great Galveston Disaster (hurricanes didn't have names yet) printed within months after the disaster and it has such gloriously fresh accounts that I can't really find anywhere else online. Admittedly, it's mostly just a compilation of government documents, correspondence, pictures, newspaper entries, testimonials, and other accounts, but I digress.
Could I land myself in hot water for using quotes from the testimonials in my work of fiction of real people or excerpts that are dated 115 years ago? I thought copyrights only lasted for 100 years, and I doubt this publishing company (which only printed this book for one run and then disbanded from my research), newspapers, or families of the deceased would mind, nor would I know how to track most of them for permission
You need to ask permission of copyright holders for as long as copyright is in effect.
That does NOT mean you can use the work without attribution after copyright has expired.
That's called plagiarism, and I'm very sure you do not want to do that (or that you even intended to, or that you thought it might sound like that.)
What you'll do: if you quote the material you CITE it. As in footnotes or endnotes.
"The Great Galveston Disaster was a gully washer of a storm, propelling man and beast like drunken sailors jitterbugging dance hall floozies down the streets." said former taxi dancer and historian Janet Reid."***
****Title, Author (Publisher: year)
When you sell the novel, your publisher will have a style guide for footnotes, and you'll follow that, but for now, this will do.
And just as a side note: keep track of your citations and PAGE NUMBERS from the quoted work in a separate document. Don't ask me why I know this. Just benefit from my dreadful mistakes.