Last year I did a north/south crossing of the park. Up the Elwha, over Low Divide and out the North Fork Quinalt. I used the Hammock all 4 nights without a problem. Keep in mind that those are both river valleys but there were endless hammocking possiblities. I even met a ranger one night and she was checking out my home made hammock and said she was starting to see a lot more of them in the park. So, no regulations against them. My last night on the hike I got all jammed up with some weekend hikers about 6 miles from the ending trail head and was so glad I had my hammock because all the tent sites were taken.
More recently just over this last Memorial Day weekend I hiked on the south beach trail in the park and although I hammocked on the beach 2 nights I also hammocked in the forest 1 night without any problems. I posted some recent photos of the beach hike in the gallery.