Well, I typically laminate thicker hardwoods with carbon fiber for benchrest stocks. This means four 3/4" boards with three layers of carbon fiber, or a 2 1/4" blank split with a 3/4" board in the middle with two layers of carbon fiber.
Here's some photos I just got of a top-quality rimfire benchrest rifle with a stock made from a blank I laminated.
The show wood is english walnut, the core is butternut, and the fore-end has black walnut on the sides.
It's better to laminate up a thick blank like this than try to find a 3" thick blank... cutting out a big single hunk of wood like that exposes you to many more risks and a laminated stock will end up being stronger and more stable (especially with carbon fiber- give it a shot).
A friend actually just told me he's got a bunch of black walnut lumber stacked up in his attic and it's all between 1/4"-3/4" thick. I'm buying every single suitable piece. I would like to make a few stocks with more layers.