You can't "recruit" the Survivor. Imagine it's 4/3/1.
Mafia: I'm Mafia. Survivor, you will help us no-lynch, because if you don't, we WILL kill you tonight, and you lose. If you do, you're guaranteed to win with us.
Now the Survivor could try to call his bluff and risk it, but why? He has absolutely no reason to put his neck out for Town here and throw away a 100% win. So 4/3/1 is a loss for Town.
So 6/3/1 is lylo if Town tries to lynch Mafia, and has a 3/9 chance of doing so. If instead, they lynch the Survivor, then the next day they'll be at lylo, but with a 3/8 chance of lynching Mafia. Better odds, and one less Townie to mislynch. Sounds like optimal Town play to me.
Optimal town play is killing mafia. There are very few edge cases where you would prefer to kill someone other than mafia. And this isn't an SK we're talking about, who keeps killing. It's basically a Tree Stump.
That's not what optimal means. That's like saying about a game of Dominion, "The optimal strategy is to get the most points." Optimal Town play is to give yourselves the best possible chance to lynch Mafia. Obviously as Town you'd rather kill Mafia than the Survivor. But in the above situations you'd MUCH rather kill the Survivor than a Townie, because if you kill a Townie you lose. And killing the Survivor actually helps your chances at killing Mafia.
I think your numbers are wrong, or we're not thinking about this the same way.
6/3/1 (town/mafia/survivor). First, I'd note that that's 3 deaths, so it's N2. Anyway, if it is day, any one town member has a 3/8 chance of hitting mafia (NOT 3/9, as you posit) with their vote (6+3-1=8). Assume mislynch + NK. Now we have 4/3/1 and scum wins. Okay. But to get to 6/3/1, that's 2 mislynches, an NK, and a blocked NK. Day 3 at the earliest. In a game with 13, 3 mislynches to lose sounds about right for an expert level game. The bigger issue is that at 6/3/1, all three mafia claim, add survivor, and win anyway.
But assume one scum lynch in 2 days. Now we're at 6/2/1 on D3. Any one town member has a 2/5 chance at lynching scum, and scum + survivor can't lynch anyone. No reason to kill the survivor now, since that just drops things to 5/2 on D4 for lylo. Mislynch and it's 4/2/1--mafia full claim and win.
I mean, I see your argument that survivor has it easier to just win with scum, so town should just kill them anyway.
But if that's the way to play it, you just auto-lynch the survivor on D1. He has no house, so you can flush him out as a group. Knowing the others' houses does nothing for you, so everyone house claims, the 13th player is lynched. That's no fun for the survivor.
If I rolled survivor, I'd claim right away and find a way to convince both mafia and town to just forget about me.