We generally just suck up the cost, because no matter how much we say the quality of food at Disney has suffered of late, once we're there and we smell all the food, we just crave. But somethings you can do...
Before you leave, buy a couple of Brita water bottles with attached filters (not a bad thing to have wherever you may go actually). Many of them are BFP-free if you worry about that sort of thing. This way you can fill your water bottles pretty much anywhere and it shouldn't taste too much like hot buttered monkey butt.
If you gotta drink something other than water, don't use them on the Brita bottles, but I'd second the suggestion of buying juice packets or squirt bottles you can add to your own water bottles or cups of water.
Even if you don't do the dining plan, try to pace your dining so you're only dealing with 2 meals in a snack. Just have a bagel or toast in the morning, followed by a fuller later breakfast that'll carry you through lunch. Or (probably more economical), have a decent breakfast, a little snack around noon, and as late a lunch as you're comfortable having, to tide you over through dinner, where you may be able to get by with something small just to avoid feeling hungry bed.
Trail's End Buffet at Fort Wilderness is consistently one of the better "sit-down" meas on property (even though you keep getting up to get your own grub). It's not the most convenient place to get to if you don't have your own car, but a day when you're at the MK, you can take a break and boat over to Fort Wilderness for lunch or dinner.
And while it's not part of the dining plan (and you can't make reservations, it's first come first served), the Garden Grove Cafe in the Swan has character breakfasts each Saturday & Sunday, 22 a head adults, 13 for kids. The cheapest character meal you'll find on property.