My gut feel: Wood should to the majors in about two weeks. I'd say "now", but the Nats must have some reason to let him "practice" AAA pitching. Crews to AAA in July, and leave him until Spring Training. House and Pinckney to AAA about August 1. Let House get AAA baseball until next June, and evaluate then.
There is nothing wrong with letting House play AA until he hits better. Compare him to Crews, who seems to be mastering AA.
That's assuming that each shows progress. As Rizzo keeps reminding us, no player is on a train that will arrive on schedule.
And maybe it is worth having an overall discussion of batting average. I think it is important alongside OPS. A low average means a player is not getting wood on pitches. My hunch: a player hitting .300 or .290 has room to hit more doubles. A hitter like Joey Gallo might hit 20 home runs, but if he's hitting .150 he is likely doing nothing between those occasional home runs.
Baseball has been played a long time, and all those managers and general managers considered average important. (I'm about to dig through that Post article on Ohtani and the Triple Crown)