Assuming 1:1 aspect ratio is for the physical screen, the resolution most likely won't be a square because of the rectangular shape of pixels. So you'll need to calculate the resolution of visible part of the screen first. After you have found your resolution, you'll probably need to add that resolution config under /etc/x11/xorg.conf.d/
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By the way, I can't simply make the whole bigger/taller as I am limited by my 3d printer's printing volume
What are you using to draw on the screen? That would determine how best to achieve this. I'd expect it to be doable regardless, but the path there would be different.
The screen is going to be connected to my pi 4 through HDMI, using x11 most likely. I'm still waiting on the lcd controller so I haven't been able to fully test the setup
You should be able to set up letterboxing using either xrandr or your window manager, although I got pretty unsatisfactory results when I searched for "xrandr letterboxing".