Although the bulk of this discussion took place more than 18 months ago, this is the first time I've seen and read the thread. I am surprised that no one defined the function of a parametric equalizer. In the best of all possible worlds, it has the job of either boosting or attenuating the signal over a narrow band of audio frequencies, through the use of filters. How narrow the bandwidth will be, and how many filters are inserted between 20Hz and 20kHz (the audio spectrum) is a determinant of cost and complexity. Each pass band requires two filters, hi-pass and lo-pass that flank the central frequency of interest for that particular pass band. In theory, this device is completely transparent, does not at all affect "tone".
However, it's obvious that it would be impossible to build an equalizer that did not also affect SQ, one quality of which is tone, due not only to inherent phase alterations that are introduced, but also to the fact that the signal is diverted through a slew of "parts". Resistors, inductors, and capacitors needed to build filters with the desired steep slopes inevitably add colorations, and so do tubes and/or transistors needed for gain and buffering functions. So, you cannot have an analog equalizer without an effect on SQ, however you want to define that. For that reason, most of us have built our home audio systems to taste, such that we can be happy without an equalizer.
In recent years, the notion of equalizing the signal in the digital domain has become at least modestly popular among those who can afford the considerable expense of the best such devices. I am surprised no one mentioned this in the foregoing discussion. I have never heard any of these in operation, but TACT Audio is one company that makes such devices, and a few well heeled audiophiles do like them. From what I read above, a really good digital equalizer is beyond the price range of the OP. Cheap digital equalizers exist but are not a way to go for audiophiles, based on my brief experiences with a few of them.