Needs to use an Atkinson dither to minimise the dither error/distraction, this would produce clearer black and whites at the expense of a little colour/shade accuracy.
Dunno what Return of the Obra Dinn used as dithering but these videos of Doom running naive 1-bit clamping immediately makes me beg for it having the aesthetic of RotOD.
Obra Dinn took a lot of experimentation to get right. The devlog for it on TigSource[1] has some big parts just related to dithering. For instance this post[2] and this post[3]. A user called Koloth also helped provide an Atkinson-like effect that works in a shader.