So, take out the railings, bolt a couple of posts to the pillars, use arris brackets to attach a top and bottom arris rail across, then cut feather edge board to length and nail on? Apologies, you're talking to a bit of a joinery noob here. What size timber would be best suited for the posts? I'm half tempted to get somebody in, half tempted to give it a go myself. I could borrow a circular saw off my uncle to make the cuts nice and quick and easy.
Also, doing it bespoke, I could go a few inches higher in the middle for a few extra inches privacy, which is good as the neighbours house is lit up like a christmas tree and some of their outside lights shine into the bedroom. An extra couple of inches would completely block it out.