I can see why you would like characters to have their own problems. I like that too which is Bosch is my fav in crime fiction. Usually i connect easy to characters with their own problems rather get hyped over the great crime mystery in the story. Thats a second for me in those type of crime books.
Great minds and all that.... You definitely need to read Burke. Make sure to start with the first Dave Robicheaux novel, The Neon Rain.
Since it's set in Cajun country, "I Guarantee" it.