As above, verify your belt and tensioner are OK. I don't know if I would throw a new belt on it right away but at least inspect it to be sure it isn't glazed/oily, and make sure it isn't loose. You might get lucky with a flush and dislodge some grit, you never know till you try.
Does your car have VAPS (Variable assist Power Steering)? Trace your pressure line to the rack, if it goes into a solenoid assm with an electrical connector on it, it's VAPS equipped. Unplugging this solenoid will give you full boost at all times and will eliminate one possible cause of increased steering effort. VAC valves can stick, body control modules can inadvertently give the solenoid voltage.
A sticky spool valve in the rack will also cause your symptoms, most often it will happen more so in one direction than another.
Jack the front wheels off the ground and turn the steering wheel lock to lock, any tight places in the rotation?
As far as your original diag, I tend to agree with you. A PS pump is a likely cause. There are pressure gauges that can be hooked up to the pump output to sheck pressure specs, not all shops have them. Diagnosing your problem without knowing you actual pump pressure is a guessing game.