I didn't read all the replies all the way through, but are you staying on-site or off-site? That makes a huge difference I think. On our trip my 3 dd's were very close ages to what your 3 oldest will be, (they were 7, 6 & 3). I guess with your ages I have 3 words for you: two double strollers! Because we were "off-site" and had never been, I had the "go commando or go bust" attitude on the 1st day of Disney, and we had a stroller for our 3 year old only. We had breakfast ressies at CRT, early, so we were up at 6, out the door at 6:50 a.m. & arrived at the gates of MK at 7:20 a.m.. we returned to our rental home 14 hours later, with two very tired older girls with blisters on their feet, and I thought we sat alot! WE did ALL of the "shows" that you can do at MK, we had our sit-down at CRT in the morning, and then we "sat-down" inside of Cosmic Ray's CS for late lunch/early supper, which we spent close to an hour in just taking a break from the heat/resting our feet. The next day, the 1st thing we did was stop and rent a double stroller, and our girls rode in one for the remainder of our trip.
My thoughts; if your staying off-site you need a little more "strategic" planning, we also didn't want to leave the parks to lose the great parking spots we had by getting there so early, so try to plan out when you will see shows to get a break, and try to do 1 sit-down meal/day, your time of year also matters, and I thought your ticker said Oct., my first trip was Oct & it was HOT!! If your staying on-site givin' the ages of your little ones, I would play it by ear but probably try & get them a mid-day break if possible, your 7 & 5 yr old might not need a break but the younger ones may, perhaps you & DH could swap days where you take the youngest back to the hotel and vs.
Good luck with your planning and just remember their your kids, you know them better than anyone, so follow their lead and it will all work out for you!

- there's some Pixie Dust and Tinkerbell wishes for you
Chip