From personal experience I think don't rush it and worry about it. Reading gets more fun - perhaps because it is more of an individual understanding - (you read alone and to yourself), after grade 4 even better - grade 5 and 6.
I would suggest some 'classic' adventure stories: most books by Andre Norton - the time trader series for example; Jim kjergaard - Big Red, later on Zane Grey.
Good luck. Have fun with those kids!
My 8yo partially dislikes Geronimo Stilton books because they're "too old" (they started in 2000s and are now mostly done publishing the new ones). The books you mentioned were from mid-20th century :)
