N.S.
I agree they're too old for a morning nap. But for afternoon nap, what I did with my kids was force them to lay down for quiet time with me while I'd feed the baby.
My kids were not big nappers at all. I think boys just aren't built that way. But I had great success in making them lay on either side of me so that they wouldn't be tempted to hit, poke, talk to each other. I'd make the close their eyes and listen to soft music for a minimum of 30 to 45 minutes. Often, they would fall asleep, and then I'd escape and leave them on the bed, while I'd get a break and get some things taken care of.
If they didn't fall asleep or were particularly restless, I'd allow them to pick a book or two and quietly read in their rooms (apart from each other)while laying on their beds with their blinds drawn. Sometimes they would fall asleep.
I agree, lots of opportunities to burn off the excess energy is really important, as is a good lunch. Plan nap/rest time, right after lunch, but not heavy playtime. Digestion helps make for a sleepy kid. Playtime can sometimes up their adreneline too much, and then they're not able to come down enough to sleep. Plan heavy playtime for before lunch, and you should have success in getting them to relax.
As for schedules, try to get cleaned up and tidy the house before the older children wake up in the morning. Put together a circuit of activities for them to do every day...sort of like prek or k...so every morning they do the same activities at the same time. That way, if you can't be there right away, they'll know what they should be doing.
Good luck.
N.