Curious as to what about a reservation process would be so off putting that you would stop going to a place you enjoy?
You would probably get a few better answers to your question if you included what you plan on doing once you have a site with river access. Do you fish, float, kayak, skip rocks etc. Do you need a boat ramp? Do you want your site to be on the water or just need the access? What area do you have in min?. I can point you to several parks in Montana on rivers, but I don't think that is going to help you. Good luck.