Is it possible for him to do 4K in the morning and K in the afternoon? Even if you know it's not, I'd throw the suggestion out as negotiation. Give them something they can say no to. Also makes you look cooperative and focuses the issue on that nap.
I suggest preparing a response if they suggest an alternate solution to address only the nap. Some advanced children can read silently during nap time, for example. Are you okay with that or not? If he could do something else during nap would 50% of your 4K concern be resolved?
