My Papst 80mm fan arrived today. It is nearly silent, compared to the old one (i.e. jet engine.) It spins a little slower, so the internal temperature sensor is reading 3C higher, but that's negligible.
Now, my computer is at a noise level comparable to the fridge, and much quieter than the pipes of the folks upstairs. The primary noise sources are now the hard drives and CPU fan.
Next step: Some case muffling, and possibly quiet hard drive mounts.