I basically do what you do; there isn't that much fluid in the system, but I don't like taking a bath in any kind of oil. I suck out as much as I can with a veterinary syringe with a small diameter clear tube attached so I can reach down into the pump. Suck out as much as I can get. Then jack the car up & support it, then turn the steering wheel lock to lock WITH THE ENGINE OFF 20 or more times until I can actually get no more fluid out. THEN disconnect the return hose and put a vacuum plug into the bottom of the reservoir. Point the return hose into a container and fill the reservoir with new clean fluid.
At this point in time, I ask my wife to get in the car, DO NOT START THE CAR, just turn the wheels lock to lock until I holler that I've got new fluid coming out the return hose. The "return" hose on my car is ~8 feet long, I think the factory calls it a "power steering cooler" since it goes up behind the radiator, makes a square "loop" then goes back to the pump. This long hose holds quite a bit of fluid. The "exchange" is now complete. Remove the vacuum plug from the reservoir, shove the return hose back on & clamp it, refill the reservoir and again turn the wheels lock to lock 40-50 times until it is completely quiet. Front wheels are still in the air so there is no "load" on the PS system.
Finally, I start the car, and continue turning the wheels lock to lock until it is for sure quiet. Let the car down off the jacks and go for a drive. Steering should be totally quiet and smooth as butter.
I know all this sounds tedious, but it actually doesn't take too long at all. I'm good for a few years and I'm probably WAY TOO OCD, but my vehicles are pushing 200K and steer as good as my daughter's car with 15K on it.