To the OP:
Very sorry for your frustration with ADRs. I tend to agree with you.
Free dining changes all the dynamics.
Just a few thoughts you may want to consider for dinner. These are a bit harder to get to, since they are at the resorts rather than the parks, but worth a try anyway.
1. Turf Club at Saratoga Springs Resort. We had a lovely lunch here, and I would think dinner is nice, too. Tasty food, and a bit more civilized atmosphere than most places.
2. Grand Floridian Cafe. Very nice atmosphere and tasty food. Easy to reach by monorail from MK.
3. Olivia's Cafe at Old Key West.
4. Marakesh at the Morocco Pavilion in Epcot. For some reason this restaurant often doesn't fill up. Perhaps because the food is a bit exotic. There is live music and a belly dancer. We enjoy it.
5. Wolfgang Puck Cafe at Down Town Disney.
6. Maya Grill at Coronado Springs Resort.
7. Captain's Grill at Yacht Club.
8. Garden Grill Restaurant at the Land Pavilion at Epcot. This is a character meal. It can be less crowded than some as you have to be in Epcot to do it. Most people prefer character meals at the resorts.
9. Lilo & Stitch Breakfast at Ohana. This is a very fun character breakfast. Sometimes you can get in if you book late morning, such as 11:00 a.m. We like it better then as it's less crowded with better character interaction.
10. Try for Cinderella's Royal Table at 3 days and then 2 days before you'd like to dine there. Reservations have to be cancelled 48 hours before or the party incurs a penalty, so sometimes you can nab an ADR due to a cancellation. Try for lunch, which is less popular than breakfast. Dinner is less popular than lunch because you don't have the princesses. It does take 2TS credits.
11. Yachtsman Steakhouse. Takes 2TS credits, but steaks are great. You'll have a really nice meal here.
Just my thought for some possibilities. Good luck.
)....I will give you some advice that I hope will be helpful. First, if you are staying on-site, speak to the concierge at your hotel and see if they can look for cancellations for you and book things as they come up, we did that last year and got into a couple of things that we didn't think we could get. Also, usually, the Cape May Cafe will get you in if you go early enough for breakfast (we have often gone without a reservation and then they took us without waiting too much). Lastly, try to get in early to the restaurants, especially at Epcot, and you have a chance. Generally, I have found certain places very accomodating, even without reservations, it just depends on how you approach them. If you are resourceful you will get in to something. Just keep your cool, don't panic, and whatever happens, don't let it ruin your trip. After all, you will not starve!!! 
I know that it is a different experience and you were both looking forward to it, but don't give up. The Mexican Restaurant is usually good about getting you in also without reservations....there are places....just be prepared to walk around and find one that will take you and go early! (Next time, plan to make reservations 90 days out, I just read another thread where the poster was going to be setting up at 3 am to make reservations at 6 am!). Good luck.
So yes, people do cancel-I did! Oh yeah, one more thing... The next time also keep in mind that if you book your ADRS online, they will start up at 6:00 a.m., so you can get a jump on folks calling in at 7:00.
Every restaurant is not booked solid...like the rest of us, you need to be flexible with your times & days, and pick from the restaurants that are available. You will have a wonderful time no matter where you end up eating.
) and then kept searching. Now I have made and cancelled dozens of ADRs and come up with almost everything my family of 6 wanted but not at the absolute perfect time 
in some instances. At this point, I plan to sit back and relax and enjoy being in the WORLD!! Good luck!!
I know planning meals 90 days out throws some people for a loop. I couldn't believe it either when I started planning my first trip.
