Congrats on planning your budget trip.
I think it fair to say that a budget trip is possible. We are a family of 7. It has been a long while since we have been.
I didn't crunch your numbers as we usually drive and stay onsite.
I think we share the same thoughts for some of your plans.
My kids would definately rather being riding the rides & playing than sitting down to table service. A sit-down meal for a large family can take up quite a bit of time even with reservations. That time, for us, could be better spent. During the dinner time hours some of the rides have smaller lines so we take advantage of that....eat on the run and ride an extra turn a BuzzLight Year

. At Disney Studios we would grab some fruit. pretzels or even large fries(McDonalds quick stand) and thensettle in to watch the parade.
Now if we had older children or even really young babies, a sit down meal is a nice break from the day, but right now it would not be a priority.
Another thing is souvenirs. We explain plenty ahead of time that a lot of the toys, etc are extremely pricey at WDW. We are there for the themepark experiences not to buy toys. So, with that explained before hand we do not end up with a battle over a light-up toy or Legos, but instead focus on the great rides and definately "window shopping" at the gift shops on the way out of the rides. I usually plan to get the kids one main souvenir as a memento of the trip. It usually is from one of their favorite rides or a special something from Downtown Disney. I let them look throughout the week with the understanding that the purchases will not be made until the end of the trip just in case they change their mind about what they want to get. It is too easy to grab a small toy the first day, only to wish they had waited because they would rather have that other special thing. T-shirts from their favorite rides is something that I really like for them to get.
The pressed penny machines are fun as souvenirs also. You could plan to let each child take a turn to get one....making a collection for the whole family. They do not neccessarily need their own collection because once home having one main set is nicer than them having something they will likely forget about. Same goes for trading pins. It is fun while you are there but once home the pins are not really that important. I know there are many people who have great collections of pins...so for them that in their passion. Its just not for us.
A lot of the focus is on the family having a great fun trip, with the happiness of actually being at WDW far outweighing any little trinket.
Wishing you lots of pixie dust.
P.S. check out the family forum also...there are many great very inexpensive or even free things to do.