Should I switch to a larger room?

For a 10x12 room, I would suggest placing 8 to 10 artificial ficus 5' trees behind, between and beside the speakers and one on each side and slightly in front of the listening position.  Maybe one behind the listening position.  These will break up room reflections and improve the sound quality of your room.  

Yeah, yeah, yeah....  I know the room will look like a section of the equatorial Brazilian rain forest, but will improve the sonic characteristics of the room.  

Even if you do move to a bigger room, using these artificial ficus trees will diffuse the sound for a tenth of the cost of a basic room acoustic treatment.

Bigger is better.

Switching rooms would be a PITA, but is it worth doing?

Oh good Lord yes!!!  And even more so with your speakers.  You can do all the mods you want, but the room will still be the largest contributor to what you ultimately hear.  And although changing rooms may be a bit of a PITA, it’s still free!  How many substantial sonic upgrades can you say that about in this stupid hobby? 

The dept of the room is very important:( you do speaking here of ft. instead of meters in the US). Take than the room with the largest dept -side, (speakers on the shortest wall ) otherwise you can have more resonance. (And  give your “basses” come across as woolly) . Try it out : the sound will be different. And take the room that sounds best to you ! Enjoy your music !