If you fish the less popular streams, you will probably have them all to yourself, especially on a week day. Monday, a friend and I fished two streams within 5 minutes of Little River, and did not see another fisherman.
And you will be surprised at how good the fishing is on these streams. The size of the fish you can catch in smaller streams is also surprising. Just study a Park map or topo maps. Finding a gem not many people fish, is a kick, and the searching is a lot of fun. There are many, many wonderful places in the park away from the main roads and parking areas.