Tunic of the Exile
It has always seemed to me that the Exile would be every bit as likely to have some kind of functional unique garment as Atton or Mira, but lacks one. Your clothing options as the exile are not overwhelmingly appropriate, either... it seems awkward to say "I'm not a jedi any more" when you are wearing jedi robes.
I was thinking a <Your Name> Jacket would be a good answer, something that could either be in the footlocker of your berth along with the <Your Name> Armband, or perhaps in the med bay of the republic ship.
Stat wise, it should compare to Atton and Mira's garments I think. In appearance, it should be unique in TSL, rather than a re-color of another character model. This is where the help of another modder would be indispensable.
What I have in mind is taking the Star Forge Robe from the waist up, and attaching it to a KotOR I jedi robe from the waist down, but with a truncated "tux tail" no longer in the back than in the front. This would be recolored to match the sleeves and hood of the top half, and the boots should match the color of the leather chest piece and gloves. The end result would, ideally, give the appearance of a hooded tunic with some protective leather reinforcement, which seems like the perfect thing for the exiled General, very functional with some protection but no restriction on movement - the kind of garment you could rely on when traveling light.
I have seen mods that shorten the "tux tail" of the KotOR I jedi robes, and many that change colors and textures, so the big question is "is it feasible to weld the top half of a Star Forge robe to the bottom half of a jedi robe?" And, since I don't have photoshop and don't even understand most of what is said in the tutorials, another question would be "Would any talented and kind modder do this for me?"