Gen 3 Hall of Fame only stores TID/SID, PID and Nickname of your Pokemon, nothing more unfortunately.
Though you might be able to recover your Pokemon as Pal Park doesn't delete the whole Pokemon data. It only sets the species ID to zero. So if you didn't move any other Pokemon onto the box slot, where the Pokemon you want to recover was before the transfer, it's data should still be there.
You can search your Pokemon by it's PID in a hex editor.
If you found your Pokemon save it's 80 Bytes into a new file. The problem now is that you can't load the Pokemon in PKHeX directly as it's species ID is invalid. So you have to decrypt it and fix the species ID at offset 0x20 as well as the checksum at 0x1C manually. Then PKHeX will be able to load it again.