We just did 7 days on the Salmon, taking out on the 12. I took both my 4wt and my 8wt, thinking to get down deep with streamers. We fished some side streams -- Bargamin and Sheep creek and had a lot of fun nailing LITTLE rainbows on drys and terrestrials. Not a cuthroat in sight. Think you would have to be willing to walk a ways for those. Saw several other decent sized creeks but didn't fish them. The ranger at the put in doesn't know about fishing so contact the Idaho Fish and game.
I spent some time stripping streamers deep with a sinking line and my big rod. All I got was a very sore shoulder. I'd leave the main stream alone unless you have a spinning rig...and want to go over to the dark side that badly.
The best opportunities I saw were at the inlets where the creeks run into the main and keep it cold. I fished at sheep creek with a number of different hopper patterns and had some intesnse "looks" from some very very big fish...but ended in refusals. I should have tried nymphing there, but left my wets across the river in camp.
You should try so find some Morman Cricket patterns, sizes 6 to 12 or so. They were all over Sheep creeks beach rocks and may elicit a rise better than my hopper patterns.
If you can camp at the South Fork/Main Salmon and walk a ways, you may have some decent luck, it looked to have some lovely riffles and was running colder. We didn't camp so I can't give you a report.
All in all, if I went back, I would probably leave my FF gear at home. We spent 100 on licencess and thats a lot for some baby rainbows.