Color space output for web GIFs

[GXGsynth]

I'm creating some 112px x 112px animated GIFs that need to fit within the 256 web-standard colors and render with a transparent background, but using the Photoshop color conversion settings ends up looking pretty mediocre and makes even static colors have animated multicolored noise

is there a corresponding output color space/workflow that will squash the output down from sRGB to web-safe 256 more accurately?

[elsksa]

That's solely a post-matter, falling outside Octane scope.
Octane will output the high quality data (e.g. OpenEXR) that can then be converted into virtually anything (e.g. JPG, GIF, TIFF). As a pointer, I'd suggest looking into FFmpeg.