Rebirth should work just fine. I moved some files around the ISO but I don't see how I could have broken the filesystem.
I no longer have access to my grey PlayStation (it's stuck in the attic at my parents' home), so I've never actually burned a PSX disc for it.
Generally speaking, if a mod won't work on PSX, it's because of some crummy disc authoring / handling software that assumes a Mode 1 CD-ROM filesystem.