No reason slave mining wouldn't work as well as in the days before the discovery of America, and logging can't really be much more of a problem there.
Ironically, this is the area that would show whether or not the planters were simply addicted to the agricultural aristocracy lifestyle or not.
Slave mining certainly worked in places like Peru. However, I suspect that the bulk of prospectors would be people without slaves immigrating from the North, and eventually they'd want to ban slavery from undercutting their work.
I'm more sceptical about how effective logging would be as a slave industry - perhaps it would work once the forest was cleared, but the original cutting down of trees seems like something that would be hard to monitor as a gang system, and it would be easy for slaves to escape into the forest.
Incidentally, which states would be ripe for logging? Surely not Arizona, Nevada or New Mexico?