A 30 second google search on "Salmon Chase book" gives over a million hits. Right at the top is this collected works of his papers and scholarly work on his life. The books are out there.
And why does it take a PhD to write a definitive work? For an example, Shelby Foote had no PhD, as near as I can tell. Carl Sandburg didn't either.
I know it is just a work of fiction, but have you Lincoln by Gore Vidal? It really is a wonderful book and Chase plays such a big role in the book as does Seward. Vidal paints an excellent portrait of Lincoln.