Pani, If you really are serious about this and plan to keep your loudspeakers, do yourself a favor and get an amplifier with significantly more power. At a minimum you are going to need 60 watts (my room is very similar dimensions FWIW).
IOW in your environment an SET is impractical. The more power an SET makes, the more limited its bandwidth- much more so than with push-pull amps!
If you really are stuck on that SET sound, get rid of the speakers and get something more efficient. The problem I think you will quickly see is there is no free lunch- as speakers become more efficient, getting full bass response gets harder and harder.
Now one of the secrets of the SET 'magic' is that they have a distortion character where as you reduce power, the distortion linearly decreases to zero (unmeasurable). Most push pull amps don't do this, but that is not to say all are like that (for example our amps share this quality with SETs). To do this generally the amp should not have a dedicated phase splitter circuit, which is one aspect that can cause distortion to rise as power is decreased below a certain level.
Secondly there is this concept of voltage gain amplifiers and current gain amplifiers. Does that have anything to do in this discussion ?
The quick answer is 'maybe'.
There are a couple of ways of interpreting this comment. Here is the first one:
Almost all amplifiers express voltage gain, whether tube, solid state or class D. Current gain amps do exist, but not in the context of audio. All speakers are driven by both voltage and current at the same time (voltage and current together are called 'power'), so if you don't have voltage gain you can't make any power.
The second interpretation:
In audio there are two paradigms of loudspeaker drive, the Voltage Paradigm which is the most common, and the Power Paradigm, which is the older of the two. See
http://www.atma-sphere.com/Resources/Paradigms_in_Amplifier_Design.php for more information. However there is a 3rd means known as current drive where the amplifier has significantly higher output impedance than the speaker. This third system never developed into a set of rules for driving speakers and remains experimental. The Power Paradigm (whether people know it or not) is fairly well accepted in the high end audio community; the Quad ESL63 is a good example as are most horn speakers, SET amplifiers and for that matter, any tube amp that does not employ negative feedback to control output impedance.