I think that a TWC civs only tournament would limit exponentially the possibile match ups, so it would be wise to have one free pick and one forced TWC pick for every game imo. Probably the TWC-forced-pick player should pick last, but i don't think this needs to be adressed now.
For the format i think that a round-robin* BO2 (every game counts, player gets 1 point per win and 0 point per loss, and every player has to pick a TWC civ at least once in every round) would make for a good first stage, with a second stage consisting in play-offs with semifinals and finals (BO3 or BO5) between the 4 players with the top score.
* every player needs to play against every other player, so this is possible depending on how many sign ups there are. Obviously with 128 sign ups there would be a total of (128x127x2)=32512 games, which is kind of a lot, and probably if every player has to play against 127 other players the tournament would last 2 years. So maybe if this is the format that you are going to use you should limit the sign ups to 8 or something like that and let the highest rated players play.
For the semifinals you could make BO3 with:
G1 TWC-vs-Free pick
G2 Free pick-vs-TWC
G3 TWC-vs-TWC
And for the finals add 2 games to make it BO5 maybe:
G4 TWC-vs-Free pick
G5 Free pick-vs-TWC
I don't know the maps so i can't give suggestions on those :/
If you don't want to exclude anyone from the sign ups then i think that round robin is not possible, you should probably stick to BO3 direct/double elimiantion or even BO1 to speed things up.
Anyway, i like the idea a lot and i would love to see more TWC civs in action! Good luck with this tournament!