Have you tried getting him to do something that involves reading but isn't?
Something like a cookery book, he's old enough to cook a meal once a week.
Let him pick a cookery book and have him plan the meal, work out the ingredients maybe even send him shopping for them.
Or tell him you have X, Y and Z ingredients and you want him to find a recipe to use them.
Or something like an electronics kit, I had one at primary school, the simple things you can just build but for other projects you need to read.
One school I worked in had a 'do now' policy, so there had to be something on the board for students to do when they came in to the room which should take 5min, one of the option was 'silent reading' so it was possible for a child to have read for almost half an hour but in 5 min slots.
I doubt you could get the school to implement the policy but could you do some blocks of reading, maybe with the whole family, 10 mins between eating and starting homework in the evening?