I run into something like this on jobs from time to time...there was a low level hiss on a system (below -100db noise rating) along with a bit of harshness. It turned out to be, in equal parts, the exotic interconnects and speaker leads picking up noise. In the IC's case, the unshielded wires were picking up all sorts of crap that the amp had to deal with, and in the speaker wire's case, picking up RF that was interacting with things in the amplifier's feedback loop.
When I replaced both sets of cables with good pro stuff, the hiss vanished, along with the harshness.
Also, amplifiers, and preamplifiers, noise ratings are usually given with the inputs shorted, or loaded. If the amp is NOT connected to anything it is just possible that it is picking up ambient noise from its inputs. This seems to be more of a problem with wide-band amplifiers.
-113db, if actually achieved, should be well-nigh inaudible except to those of unusual hearing, or speakers with very uptilted top ends.