OK, well, the grease trick worked for about 10 minutes.
I've determined my steering rack is binding up and putting too much strain on the pump, or the pump itself is on the way out. This only happens when the vehicle is not moving and you try and turn the wheel.
I had a severe curb hit a few years back and I think that damaged the rack.
I put in some Lubegard power steering additive and am just going to live with it until it totally fails I guess. It's fine while I'm moving, and there isn't any tightness in the steering.