Flydoc, I did the exact same trip today with my family but a little bit later in the day. That stream is tough to cast on but I did manage to catch 2 rainbows. They were small; about what I would expect from that stream.
There was a guy who passed my dad on the way out who had fished from the road all the way up the West Prong to Campsite 18. He said he caught quite a few. Of course he had to have been fishing all day in order to make that climb...
I decided to exit the park via Gatlinburg and on the way down Little River road we pulled off on the shoulder right before the road to Elkmont. There was a huge hatch coming off. They were all over the water and the fish were rising. I couldn't tell what they were, just that they were yellow. I tied on a Parachute Adams and climbed down into the river. I got hits on almost every cast. I could only fish for about 15 min because it began to get too dark to see but I did squeeze a few nice fish out of my trip today.