Ive done this trail twice. First thing - a trailer is totally out of the question. There is some severe hike-a-bike, and you would have to disconnect the trailer and make two trips if you were doing that.
I did it on a Salsa El Mariachi with frame bags both times. First time, I did it with car support, my wife met me at Dewey Bridge with the car for camping one night there. The other time we did it unsupported - camping near the boat launch one night, and up past Fisher Towers the next night. Water is a challenge. On the unsupported one, we took an MSR ceramic filter with, but it clogs up easily with the silt in the river. Best thing is to take a large water bag and some alum - bag the water out of the river, sprinkle alum to help it settle, and then filter out of the bag.
I would recommend you get yourself a nice steel hardtail, frame bags, seat bags, and bar harness from Revelate, a nice water filtration system, and get your total shelter/clothes/food/tools/spares system down to 15lbs or less, and hit it!