A compromise could be to render in the original PSX 240p resolution, and then apply some shaders to make it look "retro", like scanlines or imitating composite/s-video, similar to what you suggested? 640x480, while not as bad as at 1080p, can still make those backgrounds stick out.
I think in the original PC version there was an option to render in 240p but display at 480p? 480p is the lowest option in the steam version, which I currently own.
It's a shame squaresoft "lost" their original renders.