I've been thinking about this for a few days. There might be another approach.
The theory behind the Nicola method is that people who desperately need to feel included bow to peer pressure. I know this bi-polar personality. They lack self esteem and that's why they need to fit in with other people. Because they need to fit in with other people they don't have good defense mechanisms, they don't defend themselves and they easily conform because they want to fit in. Their low self-esteem and lack of defense mechanisms leads them to be incredibly passive-aggressive out of some kind of compensation. But they don't realise they are arseholes. They think of themselves as the 'nice guy' and they'll rationalise it and believe it. They couldn't imagine any reason why anyone would not see them as the nice guy? they don't rock the boat!
They don't just think of themselves as the 'nice guy' they identify as a nice guy. This is why they support selfless causes like feminism if they're a man, BLM if they're white, refugees if they're a citizen. They make a practice of virtue signalling because they feel the need to prove that they're the nice guy. Virtue signalling is akin to psychological states like a mid-life crisis where someone starts trying to act young as if it will convince everyone else, or middle-class signalling where people show off prestige to prove their identity. There is a certain desperation and hollowness to it, almost a cry for help.
So if you challenge an idea based on reason, this is not just a challenge of an idea, it's a personal attack on their identity as a nice guy. That's why they take arguments personally and get cranky and passive aggressive.
My theory is, an alternative to the Nicola line "Have I said something wrong?." When someone gets passive aggressive, we ask "Why are you being an arsehole?" This will throw them, because they have deceived themselves into believing they really are the nicest guy around and everyone else are arseholes, and we directly challenge that identity. The identity is the underlying problem, all other moral issues are secondary, and political issues are tertiary.
Asking "why are you being an arsehole?" will change the argument and their style of arguing. Up till now they've been on the offensive throwing passive aggression at you, but as soon as you suggest that they're an arsehole, their deep need to feel accepted will set them on the defensive, and they will try to convince you that they're not an arsehole, which means they'll engage in the discussion more honestly and accurately.