the ability to do some of that will depend on your room set up, not sure if you have a fridge in POP or not. For me the challenge is balancing the cost of groceries and things I might need to make sandwiches but won't use up (i.e. condiments) versus the time to make the items and the cost of eating in park. Now that it costs to check bags, that has to be factored in. We had planned to pack a bag of groceries and with the luggage fee it's actually cheaper to have garden grocer deliver for us.
In the past we've stayed off property with a full kitchen so we could eat in, pack lunch and then we'd nibble our way around epcot for dinner most nights. It worked well for us though in truth, even doing that I am not sure we were able to get it as low as you are looking for which is admirable. At a minimum you can pack a suitcase of snacks that will last you the week and avoid any of those kinds of costs entirely as well as your own refillable water bottles. If you have a car you can pick up fruit to pack without bothering with the sandwich making or dealing with the challenge of keeping things like cheese and deli meats cold if you don't have a fridge. When my kids were younger the packing of snacks saved us a fortune and a lot of whining.
I agree with taking your weekly grocery budget as your starting point to offset your food expenses but I know at least for us, that is quite a bit smaller than Disney will cost us for the week even if I cooked all our meals this trip as even with that, you are starting from scratch on ingredients.
Eating off property will save you as well, of course, but eating out is eating out and it's going to add up. Reading the menus and reviews will help you get an idea of where you can get bang for your buck on items to share. Good luck