Unfortunatly, to the best of my knowledge, there is no way to "fix" the hiss you are hearing without doing modifications to the internals of the deck . But this would void any warranty on the unit and could be expensive if you were to even find a qualified tech that would try to lower the "hiss" for you.
If you rememeber back in the days of tape decks, they were notorious for hissing problems. Virtually every manufacturer would use some kind of "noise reduction " circuitry (dolby a -z etc.) I would notice that is would lower the hissing, but at the same time , at least to my ear, it would "muddy" the sound quality, so I would usually leave the NR switched off.
The reason you hear the hiss is for the reasons Crutchfield stated and myself in previous replies.
Your options are to live with it, or mask it by keeping the treble low and volume higher then the hiss level (may not help on quiet passages or between songs/programs etc.) Or as I stated before, use a raw mid and no tweeters and sacrfice fidelity.
Now since I can not be there to hear this hiss for myself, I can't suggest that your particular deck has a defect. But since you state you only hear it at 'near muted levels" I will assume the deck is ok.
Some cheaper decks, like factory units are willing to sacrfice fidelity to lower high frequency noise, kind of like a "trade off" loosly put. I have also on occasion had customers complain to me about thier AM reception and sometimes even FM. They can't understand that it is inherant most of the time that the factory deck will seem to be performing better in certain metrics then the expensive aftermarket replacement, just a fact of life that most people are not as sensitive to this as others, just one of those things.
Like I also stated before, you might want to try a differeent deck as perhaps there is no way this one will satisfy you in it's present state. A possible option is you add a high quality 4 channel amp to your system. Find one with as high a S/N ratio as you can. (also remember not all the time are specs accurate). Have the gain set at the point where you have enough input for a comfortable listening level ,but the least amount of noise. This option may also allow you upgrade the speakers as will and still keep the noise out, or at least make it not as noticable.
I can't offer any more help for you. I can understand your concern but as I stated earlier, most listeners would probably not even notice this, or care....assuming of course that your deck is not defective, something I can not verify with the specifics I am given.
Hope this helped your understanding.