I agree with the others, by the time you pay for your taxi rides back and forth (and lose all the time it will take you to go to an off-site restaurant), any "savings" will be wiped out.
Lots of ways to save money on food!
Eat breakfast in your room (if you have a fridge, get a box of cereal and milk).
Split meals.
Order an appetizer or soup or salad (or some combination of these) at a TS restaurant (we did this at Kona, I got the seafood chowder and sticky wings for about $12).
Eat at TS restaurants for lunch instead of dinner. (Wanted to go to Le Cellier, my favorite TS restaurant, a couple of weeks ago. Did a late lunch there, got their amazing prime rib sandwich, and only spent around $11. Had a quick snack in the evening - got to go to my favorite restaurant, but didn't spend an arm and a leg!).
Take advantage of the great CS restaurants - they're not all burgers and hot dogs! Some of my favorites: Sunshine Seasons (great chicken caesar salad, and also great rotisserie chicken); Earl of Sandwich (try the tomato soup!); Wolfgang Puck Express (chicken quesadilla - yummm); Yorkshire County Fish and Chips; Casey's (mini corn dogs); Columbia Harbor House (good sandwiches and chowder). All are CS restaurants and inexpensive.
Plan your meals at odd times. We did one of the latest seatings at Crystal Palace for breakfast (10:30) and treated it as "brunch." It's a buffet, all you can eat, and all we needed later in the day was a CS dinner.
Tons of ways to save money on meals!
[PS - your fiance says he doesn't want to make ADRs for TS meals. Unfortunately, they're a "necessary evil" if you want to get into the more desirable restaurants. Go ahead and make some ADRs well ahead of your trip - remember, if you change your mind, you can always cancel your ADR. But so few restaurants take walk-ups, it would really be disappointing for you not to have any ADRs scheduled ahead of time. People really end up shooting themselves in the foot, so to speak, but refusing to make ADRs ("because we shouldn't have to plan that far ahead."). But then you probably won't end up with restaurants you like.]