Thank you already!
I've looked through everything for the 10th time after my post and only then realized there's 2 implicit effect_load calls (which I constantly overlooked) when I open the menu. Those were resulting in the file not found messages.
I loaded them via "effect_load(mat,mat->effect)", maybe that's the issue (why only on some machines though?). Happens to files read from a sub-folder or from the WRS.
The subsequent crash then probably came from an invalid effect.
The only remaining/ actual issues with bmap_process then are some crashes during level_load (which I circumvented using draw_obj and SetTexture/ ... calls) and editing FX files live. Which only is a bit annoying but not a big deal.