I love those kinds of books. They're really satisfying in a really great way.
Sacred Games by Vikram Chandra is the first book that comes to mind. It's an epic cops and robbers story. And Naguib Mahfooz's Cairo Trilogy brings you to Egypt in the 20s for a huge, sweeping family saga. And if the back jacket copy of Shantaram entices you at all, you'll probably get sucked right in to that one.
More along the lines of Carter Beats the Devil, Matt Ruff's Set This House in Order is a look into a multiple personality. The research he did really pays off. (It's kind of like Middlesex in some ways, which is a book you should've read by now and if you haven't you should put at the top of your list.) Similarly, Jonathan Lethem's Motherless Brooklyn, about a detective with Tourette's syndrome, is a great book that gets you into a brain you would otherwise not have access to.
Jhumpa Lahiri's The Namesake is a great look into a son of Indian immigrants with an unusual name. It's not super-melodramatic, but the writing is gorgeous and it pulls you along the way a compelling plot normally would.
Maybe you'd like early John Irving. Cider House Rules takes you to a different time and place, and it gives you a romantic dilemma to salivate over, too. And it's not exotic, but Richard Russo's Empire Falls gives you a depressed mill town in Maine packed with fascinating characters. I know he got it exactly right because I grew up near a very depressed mill town in Maine.
And I haven't read all of them, but have you considered the Clavell series? (Shogun, King Rat, etc.) He's less lecturey and more melodramatic than Michener, although he does have that white-guy-writes-about-the-exotic-Far-East thing going on sometimes.
I bet Steve Winter might have some suggestions for you, sci-fi-wise, but you might like David Mitchell's Cloud Atlas, which is a book that spans a millennium, telling a series of stories that are linked in mysterious ways.