Once you resolve the status of your TX permit up here, I have carried legally (WA permit) in Olympic National FOREST; you just have to be careful not to wander into Olympic National PARK. (It's legal to carry in WA State Forests with a permit, which means it's also legal to carry in National Forest lands within WA.)
There is some nice camping that's outside the park--we found it because I told the wife I wouldn't go camping anywhere I couldn't pack.