The absolute only difference between having negative ratings and the current setup is a psychological one. What you need when you rate tracks is scale. It doesn't matter if the scale includes negative numbers or not, just that the scale is wide enough. In other words, do you need 10 stars of "room" to rate, or just 5? This has been debated here before, and what we have after all of that is the current 5-star rating system.
So, right now you have 5 ratings choices (6 if you count unrated tracks as "0 stars", and you are diligent about rating newly-imported tracks, of course). Obviously, right now, you can give awful tracks 0 or 1 stars. This will work fine.
So, the debate--once again--becomes: "I need more than 5 stars to rate accurately". And again, I am jealous of your psychological stability if this is actually true. For my own part, my mood and tastes vary enough that having a 10-star scale would be utterly ridiculous.
I mean, what is the difference between 6 and 7 stars? And is that miniscule difference so accurate and important that it holds true every day, for every mood you have? If so, I envy your psychological steadfastness.
You can always use custom fields for sorting purposes if need be.