POPS has been good enough for me and my games, but I respect your different opinion.
Sadly, I don’t think you’re going to be able to patch anti-dithering into game discs, because the action replay codes are, by design, applied at run-time and are temporary in memory. That’s also how RetroArch disables dithering.
Your best (only?) option would be to use a real PS1 with Action Replay cartridge to apply the codes. I’m not sure PS2 Action Replay would work, or a PS1 action replay disc (if such a thing exists) on PS2.