Stayed 100% of my first trip to Yellowstone at Fishing Bridge back in 2004, fully reserved like you. Too cramped for my tastes, look at photos of Fishing Bridge full with RVs, rather than the post with empty spots. Have not returned Fishing Bridge since (except for dropping by for a shower or laundry). Determined that I was fine with dry camping (24'C, no toad), which opened up far more options in the park.
In the subsequent four trips, including the past couple years (August 2013 and July 2014), I started with a reservation somewhere in the park for a couple days, usually Madison if I can get it. This insures a spot even if you arrive late in the day. Rest of the nights were finding a spot at the first come first served campground in the park. Yes, except for Norris, they are all small (30 sites), but I was still able to get in if I was out on the road around sunrise, arriving before 8am at the next place. Sounds like you're an early riser anyway, so it's not a hardship.
Granted, the larger the rig, the fewer spots that you can make use of. Just about every campsite will accommodate a 24'C.
