We are a family of 5 staying at HRH for 6 nights. We too have considered the expense of eating onsite all the time. We are driving to Orlando so will have a vehicle, but do not plan to go offsite except one day and night. . . this is also for parking reasons.
We created a menu planner to help us along with this issue. We needed to know how many meals to plan for during our stay at HRH and we wanted to make sure we were able to visit the restaurants we really want to experience. We too don't mind paying for nice dinners but wanted to try to economize a bit for the other meals. There are ways, none of which are cheap, but more economical. Bring some food items with you. Some for breakfast and even some things that your family could eat after a long morning in the park to hold them over until the evening meal. Pastamore, on CityWalk, has an inexpensive breakfast with large portions that our family plans on sharing. The counter service in the parks is going to be more expensive than your typical drive through fast food, but are usually generous portions as well, you may be able to save during lunch by meal sharing. As a benefit, by not eating 3 full meals each day, our kids will be hungry for supper and may actually eat what they order
There is a book titled Universal Orlando 2008 by Kelly Monaghan, which includes a WONDERFUL dining at a glance section. This could be invaluable to you, plus the rest of the book is excellent as well. You could find it at your local library or bookstore, but I purchased ours online at
www.intrepidtraveler.com. I got a nice discount there as well.
We do plan to have a few meals off site, but most are prior to checking in at HRH, and we are going to Busch Gardens one day during our stay at HRH, so will eat all those meals off site. It seems that renting a vehicle would likely negate much of the savings of eating offsite. Since you would need a van or large SUV to accommodate your group, you would likely pay a pretty substantial rate. . . .unless you could make ressies before you go and get a killer rate.
I assume you are flying in. Make ressies with a car service (there are many here who can recommend one for you), use your complimentary grocery stop to pick up some food, drinks and a cheap styrofoam cooler, or two. When you check out, leave the cooler next to the ice machine for someone else to use. We take two coolers, one for drinks, another for food such as milk, yogurt, lunch meat, cheese, grapes, cut-up veggies. We can save on at least one meal a day and know our kids are getting some nutritional food. Besides, doesn't eating grapes, carrots and broccoli cancel out those empty, useless calories we consume all day at the park???

Sorta like ordering a diet coke with your fries
Anyway, hope this helps with your planning. Enjoy your trip!