And perhaps it might help to thin the crown to allow more light in ... but it also encourages new growth, I think, as mine have really thickened up since they were pruned to let more light in. It was nice and sunny for a year or two.
I am learning to live with the shade restrictions (or is it the sunless restrictions.)
I do not have a dog to wind things up either.
Those are really beautiful trees. Going to research the smoke tree a bit, as I do not think I have ever seen one.