I'm pretty sure the ACTUAL cheapest thing you can do would be to rent a pop-up camper and stay at Fort Wilderness. June/July is high season, so you will be paying more to go then than, say, September. (Also, you're not going to get free dining in June/July like you might in September.) So since you can't get free dining then anyway (which is never offered at the Fort), the Fort would be cheaper than two value rooms, with the benefit of a short boat ride to the MK. (And all the benefits and character of the Fort, which I love. And I think there so much for kids to love at the Fort that the values can't offer.)
For example, you can rent a pop-up camper which sleeps 8+ for $69 a night. Rack rates are $71 a night in the high season you'll be there, or $81 on the weekends. So that would cost $140 a night (before taxes) on a weeknight, or $150 a night. (By contrast, the rack rates for Pop at that time of year are $143 or $167 (wknite/wkend), so $286 a night for two (again, before tax). You may need to pay a bit extra per person over 4 ppl I think, but it wouldn't be that much. The rental places will set up everything for you, include everything you'll need (kitchenware, linens, outdoor seating, sometimes an extra grill and outdoor lighting and decor, etc), and will come get it after you leave.
Obviously, it's not as spacious, and you'd be using the comfort stations instead of having two bathrooms, but it's definitely cheaper. You could also rent a larger camper (travel trailer or bigger) that can sleep more, with more comfort, but you'll be paying around $214 a night min (based on a week) after the rental and site costs (before tax and extra ppl).
Also just to keep in mind - the dining plan is almost NEVER cheaper than paying out of pocket for food. I love the
DDP, and I enjoy the convenience of it - I like not having to think about my food budget on vacation - but it's definitely not the cheapest way to go.
(Let me know if you want to know some RV rental places, I can tell you who I based my pricing off of.)