To update: I just replaced all the original hoses in hopes there was a leak somewhere. While I had the system apart, I tried to snake-out the "cooler" section of tubing in front of the radiator in case there was a blockage. Problem here was that no matter what size wire I used, I couldn't get it around the bend and out the other end. With everything back together, I filled the system (threw in a bottle of steering additive), bled it thoroughly . . .
AND IT STILL MAKES THE SAME NOISE
I'm thinking steering box now, maybe having some resistance or restriction that's straining the pump and causing the groaning. But when the car was on stands, I checked the steering action before and after filling the system and nothing seemed odd. I'm also wondering if resistance somewhere in the steering linkage (ball joint, etc.) could make the pump strain and complain?