If bottom line is price and nothing else, bed types, resort amenities, and such than you can do better with three rooms at a value and probably at a moderate. But I would ask some other questions, about comfort, value may be cheaper, but the beds are only doubles, adults are not going to be as comfortable on say the table that makes into a bed, but kids under twelve may do fine there. The suites do give you two bathrooms, so four total, and three rooms will give you only three. But if you move up to a moderate you get queen beds and a little larger bathrooms for about the same price. If you are younger that may not make a difference but if two of the adults are grandma and papa the bigger, more comfortable beds may be much better. Also you get just plain pools at AoA, where at the moderates the pools all have slides and are fancier so with 6 kids are you going to want pool time. I have never stayed value, but have stayed moderate, so check do they have a hot tub, moderates do, but some deluxe s don't, I don't know about value, is it important, it is to me.
Another option is renting points so you can all stay in one place. But that may be harder since you are talking late summer.
My question is also, is anyone military, or retired military.you said late summer, all honorable discharged military can stay at SoG in sept and it is 30 or 40 % off. If you do knot know what SoG is, it is shades of green, a military operated hotel on Disney property. I checked to months ago and they still had suites there for sept. there suites ate twice the size of AoA and the beds are queens. If you get three rooms there I think in sept it is $95 a room and the military person could sponsor three rooms. The rooms are huge there. To find out more you have to go to shades of green web site not Disney, you get the amenities of early morning and riding Disney buses, but you lose a few amenities such as free parking at the parks, and magic express, if you are not going to use them it works great, if you are then you have to figure if the price saved on hotels is better than the free ride to Disney and if cost effective. For us it always is and we love SoG.
Hope that gives you a better idea. Your options are endless, it really comes down to is budget your only concern or is bigger rooms, more comfort, free parking, better pools. If budget definately three rooms are cheaper at a value than two suites.