I got to page 9 before I skipped to the end. So far my idea hadn't been brought up. But if I'm repeating something, I apologize.
The way to get around the gender problem with the Exile and Revan is simple: Have your character go to the Jedi Archives, or access the Jedi Archives via computer in the ship, and simply look them up. In order for that to work, the developers would have to copy every male/female portrait from KOTOR & KOTOR II, but if the game is design for the 360 that should be no problem whatsoever. That way when you come across the portrait that fits your Revan/ Exile, you can simply answer with an affirmative.
The LS/DS problem could be fixed in the same fashion as KOTOR II: simply answering questions.
Now, my idea for how to start the storyline is to have your character, who is already an advanced padawan, but in their early 20's, and nearly ready to take the Trials. You would be located at the Jedi Temple on Coruscant. After you pass the Trials and become a Knight officially, you take part in a few missions that show the Council that you are extremely strong in the Force, and gain you quite a bit of fame. You then are sent on a mission where you encounter and defeat beings that you have never seen before and who use DS powers that you've never witnessed (the Real Sith Empire's advance scouts). The Council gives you and your master the assignment of tracking these beings to their source.
Along the way to you tracking these creatures down, you run into Bastila and Carth. And as in someone else's post, you master dies, and Bastila joins your party to continue your training. How she continues it would be based on the questions you answered earlier regarding Revan.
I wrote this on the fly so if some of it doesn't make sense, I apologize. I'll be back later after I've figured out how to get some of the Exiles crew (all of them can't be in it) into the mix.