.....No matter what speaker you choose you will have a problem with your room.......
Not necessarily.
To prevent bass overload, you need to choose wisely and not get a "too large" speaker.
In rooms this small you basically have no choice but to listen nearfield. But this is not such a bad thing as it is easier to load the room, and it allows you to buy "simpler and smaller". Since you are sitting closer, you can listen at lower SPL, and to a degree, this takes the room out of the equation. The result is a greater ratio of direct to reflected sound.
My 2nd system is set up in an almost square 10 x 11 room.....not very different from the OP's dimensions.
I have zero acoustic treatments in the room.
I use Spendor S6 (a small floorstanding 2 way) + tubes, and sit about 5-6 feet from the speakers.
The sound is VERY well balanced....deep, full, detailed, and hugely musical. I find myself just melting into the music, and not critically analysing the gear. I have no problem whatsoever with bass boom, bloat or overhang. Nor is it confused or aggressive sounding d/t excessive reflections.
Get something too big with too much bass and/or treble energy, and you are asking for trouble.