I’m not sure if you’re referring to whole-class reading or individuals or both, but hopefully, something of what I have to say will be useful!
1. Try and tailor what you’re reading to their interests as closely as possible. If whole class reading, maybe do a vote on a selection of books each week? Or draw up a rota to take turns choosing from a small selection?
2. Ask lots of questions and take an interest in the answers that are given. Encourage conversation about the story as you’re reading, but make sure to bring it back to the text.
3. Set them up properly to read- limit distractions and encourage calming beforehand. I know you mentioned that one of your reading times is after breaks to settle. Maybe try and take a bit of time before pulling the book out to do some breathing exercises as a group.
This is by no means an exhaustive list, just a few thoughts which I hope help!