Let me try to explain one problem of small rooms, and then propose a way to address this problem.
First a bit of background: The ear doesn't distinctly hear every little peak and dip that you see in a frequency response curve. Rather, the ear averages out the loudness over intervals roughly one-third of an octave wide, called "critical bands". If over a one-third octave interval the peaks and dips more or less average out, that's good. If on the other hand the peaks and dips are too large and too far apart for the ear's third-octave smoothing to average them out, then those peaks and dips are likely to be audible.
In most rooms, the effects of room reflections in the midrange and treble results in many narrow-band peaks and dips that usually average out over third-octave intervals. But in the bass region, the room-reflection-induced peaks and dips are large enough and far enough apart that they stand out audibly.
Let me explain. Imagine you're listening to a single subwoofer placed along the wall in front of you. There will be one path length from the subwoofer to your listening position. There will be another path length from the subwoofer to the wall behind you, and back to your listening position. At the frequency where the difference between these two path lengths is equal to one-half wavelength, the reflection will arrive 180 degrees out of phase with the direct sound and cancellation (a frequency response dip) will occur. At the frequency where the difference between these two path lenghts is equal to one wavelength, the reflection will arrive in-phase with the direct sound and reinforcement (a response peak) will occur. There will be other peaks and dips associated with other reflection patterns, and/or with the room's standing wave modes. The smaller the room, the higher the frequency at which these too-widely-spaced peaks and dips begin to intrude.
Now we can move this pattern of in-room low frequency peaks and dips around by moving either the subwoofer or the listening position, or both. But we cannot eliminate them - we can only hope to find positions that are a better trade-off.
But what if instead of just one low frequency source, we have several? And, what if we sort of scatter them around the room so that no two of them generate identical peak-and-dip patterns? Several researchers have studied the idea of using multiple low frequency sources, and they have found that this significantly smooths the in-room bass response not only in the "sweet spot" but also throughout the room. At least one researcher recommends four subwoofers spread around the room. And the smaller the room, the more of an audible difference multiple subwoofers is likely to make.
Now it sounds crazy to contemplate cramming four subwoofers into a 13 by 13 room, but is there another way to get multiple low frequency sources into a small room? Well, as a matter of fact there is. You see, a dipole speaker can be thought of as two monopoles operated in opposite phase. So in effect, a pair of dipole speaker interacts with the room as if it were four low frequency sources, from an in-room bass smoothness perspective.
My suggestion of a speaker type that would work well in your room would be a dipole, such as Maggies, Quads, Emerald Physics, Gradient, Linkwitz, and so forth. I'd suggest setting them up slightly asymetrically - neither square with the room, nor diagonally positioned, but somewhere in between. You may have to diffuse the backwave energy in order to get good image depth.
It is also likely that a bipolar speaker (older Mirages, bipolar Omegas) would work well in your room, as the same principles apply. Once again, diffusion of the backwave would probably be beneficial.
Getting down to a specific speaker, you might want to try the Maggie MMG and see how it works in your room. I have a friend with a cube-shaped room roughly 12 by 12 by 12 and the MMG worked well in there. That's my suggestion.
The low-frequency peak-and-dip pattern isn't the only acoustic issue in a small room, but it's a start. I can talk about others if you'd like.
Best of luck to you.
Duke