That's going to be lovely as it grows in, but for more instant gratification I would have planted a Crimson King in that area, which would have filled the entire visual space in no time. I planted one at my former home on Mercer Island to replace a mature Doug Fir that PSE killed with their constant hacking. It was a good-sized tree when I bought it, but within 3 years it had grown into this glorious thing that provided shade for most of my West-facing back yard. You can see it's shade shadow, as well as a bit of the overhanging canopy, in this pic from 2008-
In any event, I always prefer vegetation for privacy over structures, so I think you make a great choice.
And on the subject of shade (and heat mitigation), I've decided to have a retractable awning made for my East-facing deck. A large umbrella has been OK for providing shade whilst we're eating outside, but the Trex decking radiates a tremendous amount of heat into the house on really hot days, even in the morning, so the awning will be great. Should arrive in a few weeks.