On-call nights and a 7 year old home at 3. Anyone manage an afternoon nap?

On-call week. Last night was two incidents back to back, I was up till 5, and I can get through the morning on chai. By 3 I'm done. We split office days between us, so on the days I'm home it's just me when he gets back from school. He wants a snack, he wants to tell me every detail of his day, he wants me to watch him jump off the sofa. Bilkul fair. I just can't keep my eyes open. Other on-call or shift parents with school-age kids, how do you get a nap in without him feeling shut out? Screen time is the obvious answer and I don't love it.