While there are always some nice stories about walk-ups getting seated somewhere, if it really means alot to you to have a table sit -down dinner at a nice restaurant, making reservations is the only way to guarantee that.
I mean, when you say, " no ADR's planned for dinner in order to keep it relaxing". Well...do you find it that bad on your enjoyment level when you know you have to be at a dinner at a certain time? I mean, I do understand it, if you have family members and small children who get very upset when they're told they have to stop having fun in the parks because it's time to eat and you have to leave now to make a dinner ressie.
If you really want the Grand Floridian Cafe, I would just have a talk with everyone in your party about it, and make sure they're agreeable to leaving the fun and festivities for awhile when you say it's time to go.
I have always had reservations on all my trips, which are super planned to a tee, so I am just used to that feeling of watching the time and making sure I plan enough travel time. It doesn't impede on my fun, but then I've been a solo traveler the last 3 trips. Before that, I was lucky in that my parents and sister all had no problem resting and taking a break to show up for dinner reservations.
I think it's totally worth whatever sacrifice there is on relaxation there is by having to watch the time and plan to be at a dinner ressie when you consider how lovely and relaxing it is in a nice restaurant vs. the quick-counter like places.