Yeah, the problem with that idea is that Bastilla, Juhani, Jolee and Carth could be dead depending of whether Revan was DS/LS.

I also think that it should start right after the second one. Or perhaps, a couple of years afterward when the Jedi Council is not only rebuilt but is sending out its fellow trainees into the heart.
Personally, I was thinking of a Fable-ish idea. It might have to adjust to fit the timeframe, but what if in other parts of the galaxy the Sith's extermination of the galaxy was still going headstrong?(Exile timeframe?) Like, there would be Siths taking Force Sensitives from their homes when they were still too young to realize moral judgement. Think pre-teen? Anyway, the Siths would be trying to convert all the Force Sensitives children before the Sith Code and teaching is all they knew?
So say there is a bunch of pre-teens on Sith cruisers to go to some Sith planet (i.e. Korriban) and on their way, a Republic ship that is holding ex-Jedi tracks down this cruiser and saves all these children with the main character being one of them?
I dunno, I think it has many flaws due to the time frame but no flaming please. :)

Edit: Sorry for double posting, but I just thought of another idea as well. What if your character was born in one of the Outer Rim planets, places that are pre-dominantly overrun with the dark side? Maybe he/she was born on a human planet and was sold into slavery by a Sith over there? Maybe your character would think this is the natural way of life and succumb to the Sith teachings or maybe they could see the wrongness of this and switch over to the light? This could also allow your character to be accepted into the Sith Academy or join the very secret resistance groups.
If your character happens to be light, what if Revan was a leader of one of these groups? The numbers were few and after performing such task of worthiness since it has to be kept a secret, you were accepted into his/her group. Or if Revan was dark, maybe the resistance group is too just stop the spread of evil since it would consume the galaxy, after all an evil char. has to have something to rule.
Almost four years later, another famed Sith or Jedi shows up on the resistance's doorstep bringing with her key members from Kotor I and II from the Ebon Hawk to help out and that is when the story really starts. If they did my idea, I would say Carth, Bastila, Jolee, Atton, Exile, Bao-Dur, Canderous and the two droids would rally to the cause. Or Canderous would either go back to his old leader or be unforgiving and be more focused on the fate of the Mandalorians.
As for Carth, Bastila, and Jolee being dead.. then perhaps evil characters would have more henchmen to choose from on the Outer Rim.

I admit you have a point - Bastila, Carth, Jolee, Juhani and a lot of other characters may be dead depending on the ending, but we all know that there's a very small chance for the developing team to cover all the possibilities from KoTOR 1 and 2. Obsidian already overlooked the possibility of Carth and/or Bastila being dead in TSL. They both had an appearance regardless of the KoTOR 1 ending you chose in that conversation with Atton on Peragus.
If you chose the dark ending, you would see Bastila's message on Korriban (that holocron behind the sealed door in the Sith Academy) and if you chose the light ending, T3 would play Bastila's/Carth's message, plus they both appear on Citadel Station after you destroy the Ravager. Another example of these overlooks is on Korriban, when you hear the recent history of Naga Sadow's tomb. Kreia says that Revan defeated Uthar Wynn, even though you can chose to support him or Yuthura in KoTOR 1 (if you support Uthar, only Yuthura dies).
Now, I do admit my idea has flaws, I think the biggest one is the way Revan returned to Republic space, but right now that's all i have. If I think of something better, I'll be sure to post it.

Statement: Did you hear that meatbag? I'll be back!!

That is an interesting idea you had that I read and you do place a valid point that not all possiblities were covered in TSL. The beginnning you have does make it sound a bit like KOTOR where the amnesiac was Revan you just find out later. It would be a valid idea for those who want Revan as the PC in KOTOR 3, you can play Revan and get your powers back, etc. Still I have a feeling that it will be a search for Revan but it will be someone that was touched by either Revan or the Exile and they become trained as a Jedi.

You are correct. I mean, for light side female Revan characters.. some girls might have thought Carth was an idiot or did not want a love interest. But I am sitll a strong advocate on finishing the character's storylines. They already skipped over some possibilities in the second one, so why not do the same in the third? Jolee, Disciple, Handmaiden should make appearances at the new temple (perhaps Corsucant) and stay there to help the Council regrow instead of joining you on your quest.
Canderous/Mandalore probably would be too busy to join you again for another wild adventure since he keeps putting off the Mandalorians. Or maybe he will to confront his old master.
Carth, Bastila, Visas,Atton, Revan, Exile and the two infamous droids should definitely be party members. Maybe a total of 6 members that came from Kotor I and II depending on the gender of Revan and the exile.
That way, they would have less members to think of at least. It's always nice to see familar faces and feel like you have had a completed ending with the trilogy concerning all the characters. Whether they die or get married to their loved ones, I don't care. I just want to see them in there. Have the best people from I, II, and III united to fight one of the hardest enemies they have ever had to face.