Thus, the title of this post - How to DEFEAT the Square Room Syndrome.
I think your questions have been answered already. You CANNOT defeat the Square Room Syndrome. Right, so maybe you can help ameliorate the square room syndrome.
They've already told you to look towards treating of corners, boundary-meetings.
My advice, if you really want to try to tame the room some, is to corner trap, massively, yeah going superchunk. If you only have a pair to treat in mind, do the front wall, but you'd want to all the corners really. Think massive.
Regarding the door, I would put beefy panels at right angles, including treating the door itself.
Whatever you do, this is your room, so trust your ears. Just because the bass response might look horrible on a graph doesn't mean it can't be an enjoyable setup.
You can treat first reflections too, but it's the massive modes that are the biggest issue here. You suffer a doubling of your room modes since two dimensions are the same.
What's tougher is that not only is this square, but it is a smaller room being square.
Think overkill with basstraps. Focus on bass first, not first reflections for now.
As with salt and pepper, you can just add to taste. Build/buy your massive treatments, and pay attention to the SQ as you continually add them.