My post got lost too. My question for the OP is what is the height dimension of this square room? I think it would be prudent to install floor to ceiling bass traps in the corners and treat the reflection points (side walls, back wall and ceiling) with some absorption and diffusion. I think this will be a tough room so try your existing speakers first.

Regards,
Bill

Theater: 861v8+ID41, 218, (2) DSP8KSEs, DSP7200VCSE, (2) DSP5200s, Marantz UD9004, (2) JL Audio F113s, Roon
Whole House: 218s, DSP520s, DSP 320s, Roon
Office: 218, DSP3200s, Roon