While this does not appear to be an official format as described in the list provided by FFG, this had been the most popular Archon format our small group has played so far.
2 Archons, No repeating houses, Best of 3, must win with both Archons
Basically bring two Archons, neither can have any of the same houses as one another.
Play best of three format. Once you win with a particular Archon in a round, you cannot play that Archon again in the same round.
So I bring two decks, neither containing any ovelappong houses:
Deck A- Logos, Brobnar, Sanctum
Deck B- Did, Shadow, Untamed
In round 1, I play Deck A and I win, so now I can only win the round by winning with Deck B in one of the final 2 games of that round.
In round two, I lose my first game with Deck A, so now I have the option to play it again in game 2 of that round, or play Deck B and then come back to Deck A for the 3rd and final game of the round.
We also play where both players reveal their first Archon at the same time in game one, but, the loser of game one gets to see what the houses of their opponent's deck before picking which Archon they play with in game 2.
So what is everyone else doing and which formats so you enjoy the most?