I think the game can be cleared as early as Hall 5.
>2 shelters
>3 phones, each with 1 death card and 2 life cards
>1 life card from each phone given as A > B > C > A
>each of the phones spends their death card also as A > B > C > A
>remaining life card from each phone given as A > C > B > A
>all 3 phones spent their 7 cards, game clear, the two shelters are irrelevant after this point
The game says "you can only USE one life per room", but it didn't mention anything about giving ONLY one life.
Depending on how the "give more than one life" works, the real tragedy is that all 6 could've cleared the game from the outset by every phone giving to every other phone.
EDIT: The other requirement for game clear, "avoid all alien invasions", may or may not demand a slaughterfest. It all hinges on the rule of giving lives.