Searching for the most "accurate" speaker (below 15K)

My personal favourites would be the Quad electrostats or the top models from Harbeth. Both potentially supported my multiple subwoofers.

How big is the room?

In a room of that size you do not want too much bass. Something like a Harbeth M30.1 is the maximum of what a room like that can handle before you will suffer from pretty bad room modes. Even so, I would investigate dsp room equalization.

I think here the room really is the elephant in the room. 20 sq m is small, and too small for great dynamics or deep bass. That is just physics. Depending on the precise dimensions, the Schroeder frequency will be somewhere in the range 175-200 Hz. Below that, there is trouble. Put some full range speakers in a room like that, and you will regret it: you will suffer bad room modes at quite high frequencies compared to bigger rooms, and their upper harmonics as well.
So I was thinking that perhaps you should start bottom up: how can I get quite extended but very clean bass? Only when you have sorted that can you move to mid range etc. As others have said, bass traps may help, but in a small room there is little space for them (and perhaps even less tolerance). So you have two options. The first is to avoid much deep bass altogether, using mini monitors like the Harbeth P3ESR. Perhaps you could move up one size with something like the Harbeth M 30.1 that I suggested earlier, but that is about it. But there is an alternative, and it is to use multiple small subwoofers, at least two but for the best result four. See here for some introduction to the relevant research: http://www.acousticfrontiers.com/20101029using-multiple-subwoofers-to-improve-bass-the-welti-devanti...
By themselves mutiple subs already give a much smoother result, but if you then add dsp room eq the benefits will be available over a much larger listening area.
After that, and I think only after that, is it time to think about the main speakers. Avoid getting big ones for that. If money is not tight, the forthcoming DSpeaker X4 pre amplifier/DAC/room eq may be interesting as it gives you the opportunity to also equalize the bottom end of the main speakers. But realize that the higher the frequency that you equalize, the smaller the equalized listening position.

I get the impression that few posters realize that under 20 sq m is actually a very small room, both to physically fit some of the larger speakers, and to make them sing without room modes. 20 sq m = 215 sq feet.

Depending on what you mean by large, you are wrong. Room modes are peaks (and nulls) at the resonance frequencies of the room. The smaller the room, the higher the frequency this occurs. Hence, using big speakers with a lot of low frequency output is asking for trouble.
There are five ways to deal with this:
1 use a bigger room
2 use bass traps (hard and ugly in a small room)
3 avoid low frequencies altogether, by using mini monitors (the only possiblility in really small rooms).
4 smoothen them by using multiple subwoofers
5 equalize them

In a small room the best way to proceed I think is a combination of the last three options. Multiple small subwoofers can give you enough extension for anything other than mega bang HT, and are a lot smoother than two main speakers. They can be located discreetly for best bass response and that is unlikely to be the best spot for midrange image. Avoid subs that go very deep.
Use room equalization like the Antimode 8033 to smoothen the response even further. Here, the use of multiple subs is particularly beneficial. The higher the frequency, the more localized the equalization will be. So if you start with a wider listening position by using multiple subs, you have a much better starting point for equalization. For the same reason, you do not want the main speakers to go very low.

There is one alternative to all this, and that is to use dipole speakers like the Quad electrostats (only the smaller 2815 in a room of this size). Dipole speakers excite far fewer room modes (which is why they sound so clean and neutral). However, they are pretty massive and need a bit of space behind them as well.