Might check with Backcountry Horseman Washington--Buckhorn.
Some of the trail building groups would likely know too.
There's a guy Rod? that packs with mules to do stuff in the park/forest. He does/did a lot of trail work--packing logs/gravel/tools. Think he was the one that packed in all the gear that wasn't flown in to move the Enchanted Valley Chalet. I think the additional hoops for the park keep the list small.
The park might know, too. The guys that run the mule barn on the Elwha may know who has the permits. There was also a pack outfit over in Beaver that use Alpacas, they might still be around.
