It's that darn cheekpiece that presents a problem. Just not enough width to make a decent shaped cheekpiece. I've built a number of rifles from 8/4 planks I get from a local hardwood retailer, but none of them have a cheekpiece. The actual measurement of the wood is usually about 1-7/8". Some gun styles don't even have a cheekpiece, like an original English scattergun I own. I'm sure there are other styles out there. And it wouldn't be the end of the world if you built a nice rifle without one, some shooters just don't like them.
Also, with random planks like the one you described, sometimes the grain pattern isn't condusive to building a gun around it. Check the grain direction in both directions (vertically and horizontally) for run-out potential, especially in the wrist area.