Take a hard look at some maps. Toutle, Coweeman, and Winston units are all in that area. Toutle is draw-only, the others are open in the general season.
When I moved to the area several years ago, I took my rifle out for the season. That was the last modern firearm season here for me... lots of pumpkins, no elk. That said, we have some of the highest success rates in the state--general and special permit. It's a cool area to learn. Good luck!