All good advice...
I'd just add that even at older ages, kids still take a bit of time to adjust to school. The new schedule, people, homework etc. My kids behave at school and as soon as they get off the bus they unleash into something else. It's like they have to get all that stress out of their heads and bodies after being at school all day. And yes, bedtime is also an adjustment.
Over the years some things I've done to help that you might try if you decide to keep them in school -
Let them play hard after school - run around yelling if they must. It's a great stress reliever and even 15 min. of all out crazy play (safe of course) really seems to help them unwind.
Start wind down time an hour before bed. Usually my kids are done with homework by then and instead of letting them run around, I have them play a quiet game, read with them, or some other quiet activity. I've found if they are really active before bed, it takes them longer to settle down once in bed. I typically have them go to bed at 8:30 and by 9 they are usually asleep.
Another thing I do that seems to help them with the mental tiredness is fish oil vitamins. Obviously talk to your doctor about it, but for us I truly do notice a difference. (they make them with the gummy kind so the kids don't taste the fish)