This kind of reads like a deteriorated gear box. The pump seems fine since you say the steering effort improves with a little throttle. Higher rpms drives more fluid pressure. I'm assuming, since you didn't say, that the gear box is original....with that mileage! I'd say kudos to that life and you need to just get a RedHead gear box.
Just a hunch going on your post here. Have you taken it to a shop you trust?