Checkout backstabbr. It's a web based version of the game and allows a lot more asynchronous playing. It also allows you to remain anonymous which helps with biases and super judicial alliances.
For those on Android, check the conspiracy app. It includes about half a dozen variants as well, ranging from 2 players (cold war) to 15 (known World 901). Great platform to play.
You really only need 5 people. I haven't played with seven very often and I didn't find it improved the play much, if at all.
Just as much, if you set a hard 15 minute time limit, you get the play down to 4-5 hours (especially if you also say victory is preponderance on the board, not total elimination of all other players).
Reach out to me, I've designed a card based version that plays 3-6 and about 15 minutes per player. It is super solid but I'd always love more feedback.