5 Townies
One of the Townies is randomly chosen to be the Target, known only to the Mafia during Day 1.
If the Target is lynched Day 1, the game becomes a normal Vanilla game. (EV 2/15 for town, who are in 2:3 Vanilla, LyLo)
If there is No Lynch Day 1, the Target dies and the Mafia do not get a kill. (EV 1/3, 2:4 Nightless)
If a non-Target Townie is lynched Day 1, the Mafia do not get a kill, and the Target gets a one-shot kill instead (finding out they are the target). (EV 1/2 for town, this is either 2:2:1 Nightless with Named Townie or 1:3:1 Nightless with Named Townie)
If Mafia is lynched Day 1, no one gets a kill but the Target finds out they were the Target. (EV 4/5 for town, 1:4:1 Nightless with Named Townie)
(Total EV for town is 8/15, assuming a random lynch Day 1 - a bit better than No Lynch, and of course with No Lynch there is less/no information generated.)
In some ways this is an inverted version of Lynchpin (though they were developed independently; I have actually run this setup already in SEKKRIT PLACE with Mafia winning from a non-Target Townie lynch and Target hitting Mafia). I list specific numbers for this one because I haven't calculated EVs for any variations on the counts (and also because I may want to tweak some of the cases). Should be easy to throw in a spreadsheet, since all the cases lead to either Vanilla or Nightless with Named Townie.
The goal of course is to make Day 1 more meaningful and force information to be generated (since with 7 players, the game isn't lasting long). The Mafia have a significant incentive both to avoid being lynched and to lynch the Target, with most games likely going to the middle ground of a non-Target Townie lynch. Looking town to the Target is also very important for the Mafia's chances.
One other interesting aspect of this setup is that in the most likely scenario (non-Target Townie lynch and Target misses), Mafia have the same EV if they counterclaim the Target and if they don't. Would be interesting to see whether they chose to go that route. (And if they do counterclaim, the EV remains the same whether the group chooses to lynch among the Target claims or among the other three.)