Being a couple of high school teachers, we have never had the opportunity to go while school is in session. Lots of summer trips and a few long weekends (MLK, Thanksgiving) and one Christmas/New Years.
In regards to summer trips, here is our modus operandi (bearing in mind we always stay on site). Get up about an hour plus before whichever park has morning EMH opens. Get moving quick with a very light breakfast. Hop on the bus about 45 minutes before EMH park opening (we drive everywhere so we don't have to wait for busses and since parking is free it is much more convenient everywhere except MK). At EMH opening, hit all the headliners in that park and maybe a few other attractions. Usually about 2-3 hours of touring. That's when it will really start to fill up, so we book a late breakfast TS or hit one of the nicer CS. That means from about 10:30-11:30am we are relaxing in an AC restaurant (or at AK, this is when we hit Lion King or Nemo shows). Then we usually do one or two more attractions before we get out of that park by noon. Time to head back to the resort and do some pool time or hit DTD for shopping or maybe even some mini-golf or bowling. For us a mid-afternoon nap is almost always part of the plan. Then early evening we are headed to the park with evening EMH. And THIS is where we have booked our FP+ for the best things we can get. Depending on dinner plans, we are into the park some time after 5pm, with 3 decent attractions booked for 6-9 or 10pm. Then late night touring until whenever the EMH are.
Mornings are when you are going to get headliners done, evenings will get you one (or maybe two depending on the park) headliners with FP+ and then during EMH you should be able to hit most of the C and D ticket attractions and shows. With a daily nap, those nights of only 5-6 hours of sleep won't be too tough to survive. We almost always wake up early at Disney even if we have been out late because we are too excited to sleep in.
Since you listed a full week of a visit, that should be enough time to hit all the things you want to do and still have a relaxed vacation type time. Best wishes!