I don't think the problem was 3 mafia so much that it was 3 mafia plus 3rd party. Doc tied to lover effectively means there is no doc (because who else would he protect?). BP doesn't help much because once outed it's useless (virus's half-claim would either tip them off or lead to a distrusting lynch) and the JOAT doesn't have much ammo with two educated guess investigations and a busdrive (highly unwieldy and with so few PRs, not useful), especially when mafia have a blocker to counter any one of those. Again, maybe if I had been town (or already had the mole WC) it would have helped.
As far as not expecting one particular person to get lynched Day 1, that's also a flaw. I think balancewise you have to plan for a lynch, and if you do that, there's a 10% of any given player getting it. The safety measure kind of negates that, but you shouldn't need a safety measure.
Thinking about it, it could have gone worse: Lynch IB-->Block NoS-->Kill Zivel-->Snipe TFO-->Endgame on D2. Relies on getting lucky but it shows a possibility that needs to be planned for.