To clarify my position, I believe if the game enters a state unwinnable by town(2 players standing), or achieves the puzzle solution, the game immediately ends, with everyone as is.
It's a position I agree with.
2 players (I assume you mean 1 possessed, 1 town?) means scum wins. It would make sense to push things along rather then doing the 'D5 = No Lynch, N5 = Town Dies, D6 = No Lynch, N6 = No Kill, D7 = Puzzle Solved!' route - especially since D5 onwards would be one person playing by themselves.
Likewise if we don't lynch and scum get's there win con or, alternatively, we lynch the possessed player and town can win unopposed there really is no reason running through the extra N/D/N/D cycles needed to complete the puzzle.
Your logic actually ignores the fact KoD has tried to say that the game wont end until puzzle completion, and thus with a possession every day, scum cant win for themselves at this point, only the next player..
Honestly? I'm kinda ignoring KoD at this point (sorry KoD). My math doesn't need to account for his current string of arguments. Your death guarantees towns victory - so long as he refuses to shift his vote off you (for whatever reason) he is helping town. I appreciate it isn't exactly an argument you will except (I'd be amazed if you did) but I feel it is the best option. Sorry about that.