I have a home in Hood River, so I do fish the Deschutes a lot. I've fished the river since 1983. I don't nymph or fish dry flies over spawning or recovering fish.
If you nymph the river at this time of year, it's a good idea to find the little bank points, fallen trees and rocks that create current seams that spin out into deep water right next to the bank. These are not spawning spots, and they also frequently hold nice fish.
As for dry-fly fishing, I usually fish the eddies and soft bankside water, and I don't fish areas where mending fish are feeding.
I love Oregon's Deschutes above all other rivers. That said, I do flirt with Washington's Deschutes as well....