welcome to the forum. Me personally, having a hard wood deck myself, I would've just put the decking up as you have then hit with a gurney to clean all old dirt and crap out, then either used a scrubber but there is a lot of tinber there to be stubbed then just used cabots decking oil. The fact that it doesn't get direct sunlight by the looks of things would be a bonus
it looks great by the way.