Here's my analysis:
If you go with the dining plan, you will need to go with the Deluxe Dining Plan (DxDP) instead of the regular
Disney Dining Plan (DDP).
The cost will be $79.99 per adult and $20.99 per child (ages 3-9).
Anyone on the adult plan can order from the regular menu. Anyone on the child plan must order from the children's menu.
For the purposes of this post, when I refer to the dining plan, I mean the Deluxe Dining Plan.
The dining plan includes 3 meal credits, plus 2 snack credits per person, per night of your trip. You must purchase the plan for everyone on your reservation for the entire length of your reservation. The plan also includes a resort refillable mug for each person. Since you are staying 7 nights, you will get 21 dining credits, 14 snack credits and a refillable mug for each person for you to use over the course of your entire trip.
Each meal credit can be used as either a counter service or table service.
If you use it as a counter service, it will include Entree, Drink and Dessert. If you use it as a table service, it will include Appetizer, Entree, Drink and Dessert. (BIG meals).
Right now, based on your post, you have ADRs for 19 credits per person. (I assumed that you were doing the Big River Grille 3 times during your trip). This would leave you with 2 dining credits that you could use at either a quick-service dining location or table-service dining location. Perhaps there were a couple of other places you wanted to make reservations at? Or even make a reservation for a signature dining? Get an extra breakfast or two?
Here is also my breakdown for how the dining plan saves you money:
I find that your typical meal at disney will cost about $40 per person, with taxes and such (not including tip). I do include drink, entree, and either dessert or appetizer as part of a meal.
You are committing to Disney that you will pay for 2 table-service meals per day (entree, drink, and dessert). For this commitment, and you pre-paying for it, Disney will give you (for free) one free table-service meal per day, 2 snacks per day, a resort refillable mug, and appetizers for all your meals. For this $80 daily dining commitment, I (average) that disney will give you about $64 per day of freebies ($40 for the dinner, $3 each for the snacks, and $6 per meal for the appetizers/desserts). I didn't add in the cost of the mug, since this is a "one-time" freebie and not a daily freebie. I just consider it a non-counted bonus.
Now, appetizer, entree and dessert for each person, 3 times a day is a LOT of food. Chances are pretty good you won't order that much. Or you will gain 20 pounds each by the end of the trip. Deduct what you won't eat from the amount of freebies I mentioned (appetizers and desserts, I assumed were $6 each, meals were $40 each, and snacks were $3 each). For example, if you don't think you'll do the appetizers and desserts from each of your meals, then subtract $36 per person from the freebies each day. If you think you'd only use 1 snack per day instead of 2, then deduct $3 from the freebies each day.
a "quick and dirty" way to calculate which way is better: Assume that each of the meal credits would cost you $40 each to order off the menu at the various restaurants...most sit-down places cost $40 each for a meal for each person (including taxes, drinks, etc.). The places costing 2 credits each would probably come pretty close to doubling that price. So the approximate cash cost of paying out of pocket for each of your meals would be $40 x 19 credits = $760 per person for the trip. The cost of the dining plan is going to be $560 per person for the trip. This means the dining plan just saved you at least $200 for your trip...Now add in the cost of snacks, sodas, ice cream bars, etc. at $3 each to calculate your total savings.
If you were to go with the Tables in Wonderland card: the card would save you $152 per person for your trip (minus the $75 cost of the card, and potentially the cost of having to upgrade one of your tickets to an annual pass).
The calculations only work well if your dining habits somewhat follow the pattern of what you can/should eat under the dining plan.
Also remember that everyone in your group pulls from the same pool of dining credits. This is especially useful for snacks. For example, if your kids go through lots of popcorn, ice cream, sodas they might need 3-4 snack credits each per day. Whereas if you and/or your wife/husband really MIGHT get a soda every other day, then other people in your group can use your credits. It can also be useful for the 2 extra dining credits you would currently have extras for if you have one or two of those bottomless-pit teenaged boys in your group... they could get a counter service of their own when they go off exploring.