I'm with Reggio....he should be able to rest just fine. I don't care if a child is 15 in my care....he's still having quiet time, lol. I need a break from them, they need a break from me and really, they all need a break from each other. It's awesome that you don't have screen time. I'm impressed but not as dedicated as that. We don't watch any television right now, save the odd movie as now I only have babies who all sleep. When I had older children, they had to lay down and watch a movie. Each had his/her own pillow and blanket. 9 times out of 10, they fell asleep part way through the movie just because they were forced to lay still and realize 'hey, maybe I AM tired after all". Right now, your little guy has the option of going to the bookshelf and he's likely to milk that for all the entertainment value it's worth.

If you feel willing to cave on the movie thing, pick the movie a 3 yr old would find the most boring ever. After a couple shots of this, trust me, he'll sleep 11 yrs and I've not had a non-sleeper yet.