I took the shop's word for it when they said I needed a new P/S pump. After Tomguy's response I decided to check the P/S fluid. (Yes, I'm a novice.) When I found and got the resevoir open, I discovered that it was indeed low on fluid... I purchased some Dexron, topped it off, and now the horrible moaning-sound-while-turning has stopped.

Do you know if it could still be the case that there's a problem with the pump?

I'm going to give it a bit, check the fluid level again, to see if there's a leak. Either way, thanks Tomguy!