Even if you have a special SG costume, you can still enter SG mode while it is on, no? I'm assuming (probably shouldn't, but meh) that your SG costumes have matching colours, so it is pretty easy just to have SG mode on while you are wearing it.
On the prestige over influence, it makes sense concept wise (the more recognizable the SG the better the base) but as far as in game goes, it just seems too easy. Maybe instead, you should earn prestige when you defeat villains while you are in a team with one or more other SG memberes.