I reread your post just after I posted back to you and realized that it does make the noise stationary. Sorry about that!
Does the noise that it makes over bumps sound the same as when you turn the wheel?
Or could it be near the base of the steering column at the driver's floorboard, a light squeaking sound?
The suspension noise you described is what I was trying determine if you had, and now I'm sure that you have more than one noise and that's not the one you are after. The mattress spring type noise does sound like it's probably one of the ball joints that you haven't gotten replaced yet.
Since your other noise definitely isn't the same as the one outside, from your descriptions I believe your noise may be inside the car. At the firewall where the steering shaft goes through there is a rubber boot. This seals the shaft and doesn't allow air or water into the car. This is a fairly common place for noise when turning the steering wheel. The rubber rubbing on the steering shaft will give a squeak. Take some penetrating oil and spray down the boot where the steering shaft goes through, run the steering wheel fully in both directions a few times and see if the noise subsides.
Once in a while you can have noise from the input seal of the steering rack, which is right below this boot at the firewall. If lubricating the boot doesn't help and the noise is coming from that area you may have to remove the boot to expose the top of the steering rack and then run some lubricant into the top of the steering rack seal.
This is the area where the boot is. The boot is missing in this picture.
WD-40 should work ok to lubricate it.