The park has some nice water, especially if you are willing to walk a while away from the main fishing spots. In my experience, it can be very crowded, even during the week. I like the Montana idea, but I might stay away from the park, and I would definitely move the trip back to the last week of June, or the second week of July.

Also consider Colorado. Although I admit I am a bit biased, I think we have the finest small stream fishing in the country, along with enough big fish / big water destinations to make the trophy hunter happy. Access is very good, and the camping can't be beat.