Basically I agree with everything Zack and Thomas said. Something I think really needs to be stressed: tweaking/getting rid of FTL travel is not likely to change the RP much at all.
Now I don't read the Sakura, but unless JP sessions start with "10 minutes after the last JP...." then your character would probably have been sleeping. Your character doesn't cease to exist when you stop RPing it for the night. If that's how the JPs are actually handled, then that's something your character should take up with command, because it's pretty foolish to expect your soldiers to run without sleep because you can move all over a galaxy within an hour.
Social RP should really be done without a GM anyway, unless you want to interact with NPCs, which could be all right or pointless depending on how it's played. If you do away with FTL travel, you know what'll happen? JPs will start taking place a few days later IC--maybe just hours later--and you're still not going to have social RP. That's because when GMs start JPs, they're working towards a goal. That goal is hardly "let the characters socialize" because the players can do that without the GM.
As for space exploration, how do you plan to do that anyway? It's not going to be like "now that we can't move so fast, it'll be so much more intersting!" You're just going to be moving slower. This RP system isn't made for your characters to be out mapping the universe. It's like that old Investigation Board. The Empress' suicide was not meant to be investigated OOC. As a result, there was nothing that could really be investigated. Now OOC shouldn't really impact IC, but if it's how the game is played, you're just going to have to accept it. Until someone comes up with a new system to do it--which seems rather unlikely to me--you're not going to have "exploratory roleplay."