bnses 087 as recommended by Tom works fine saving, closing the emulator, and reloading. The time remains intact. It's using that XML file that came with the patch. The .rtc file that's written to disk is 20 bytes.
Using the manifest.bml that comes with the patch, or the one auto-generated by Higan (in the case of the Japanese ROM), the .rtc file on disk is 16 bytes and they look quite different when comparing them. In-game, doing the initialization and then setting the time will allow the game to work just fine up until the first time I save and close the emulator, and from then on the date is reset to 0-0-2000 every time I load the save.