As someone who is a fan of gift cards (particularly as I was getting up to 9% off), I would agree with others and say don't do it. For me it worked because I had a one-night room to pay (came in earlier than planned for a DVC rental) and was paying for all my food, etc (and knew I'd go back in a few months and/or I occasionally buy from
ShopDisney - so it was okay if I had extra, which I didn't). That said, my style was more 1 TS (enjoy breakfast out) and 1 QS, and usually 1 snack. I bought a couple of souvenirs but I did it using my Disney Visa Debit, where the 10% was better than the 5-9 of the gift card. That said, my general estimate/spending was:
Day 1 - Epcot (Space 220 Lounge, 2 F&W purchases, Regal Eagle kids meal) - 80
Day 2 - DHS (3 snacks, no meal, no extras) - 18 (I also ended up renting a wheelchair, which wouldn't really add up for you all)
Day 3 - DAK during day and MK for Boo Bash (Rainforest Cafe and Yak and Yeti, both 0 via Landry's Select Rewards, 1 soda at DAK, 0 extra at MK as I used the included drinks, etc) - 4.50
102.50 for food for me (for 3 days). Since you said no souvenirs, I didn't include mine. So, if you did the Gift Card at 5% off, that would net you 5 dollars. If you end up under-spending, however, it's just a wash at best. That said, based on what you said and my experience, I'd venture 150/day for food for the four of you (~32 pp for 4 people, plus a little more for snacks/adult drinks) - making 600 a decent average. Maybe just plan to get 500 in case you share meals, aren't as hungry, etc?
(And then on the other hand, I didn't see if you planned to do things like G+/ILLS. Any extras you might get at the last second, etc. - but if you want to be as conservative as possible while still getting some discount - I'd aim for 4/500).