You don't need FTP to get locked saves to work, you can use your computer to do this. The thing is that each save is constructed differently and some work by simply doing as you mentioned, replacing the PARAM.SFO with someone's.
But most games (especially now) are encrypted and read other things aside from the PARAM.SFO. So it's hard to say without analyzing it first, maybe FF13 has another file that also reads from the original user who created it so just replacing the PARAM.SFO could not be enough.
PS3 Save Unlocker doesn't require a JB since it's a program for Windows. Now it actually working is more of 70/30 chance. It's hard to say.