I don't know the Royal Gorge, but the Lochsa is tough to beat for a day run.
Plan for for the Lochsa memorial day weekend, if you want the added excitement of a lot of people watching from shore. That is about when it often peaks, or the weekend before. Regardless, you want to hit it from mid May to mid June for the bigger water.
I recommend Bearpaw as a guide, Justin (owner) rocks, they go the biggest, NEVER sneak the falls, and will take you on the full "dirty 30" if the water is not "too high". Once the river gets to 6 - 6.5' they don't take people on the upper sections, unless you are a repeat customer and up to the task.
I am a river, babe - I've got plenty of time, I don't know where I'm going, I'm just following the lines..... - "We are water" by Shaye