You may be correct in your thinking and you may be very effective in your approach. There is no one way to react to new understanding, and there are many different beliefs that contradict each other and the bible contradicts what is written. Some people read from the bible what they want to read and seem to be blind to the things the bible has printed on the pages they do not like. The old "smorgasbord" bible.
I would say to trust your instincts. A gentle, Socratic method may work for you and I sincerely hope it does.
As for myself, anger remains too close to the surface for me to be gentle and kind. Some tell me I am wrong in my technique, however, my honest, sincere thinking leads me to say what I think and be as clear and specific as I can possibly be. Contradictions cannot be denied, nor can incongruity, and inconsistency.
Be sure to develop a thick skin because no matter what you think or do, someone will find fault with it. In many ways false accusations make you stronger; another's honest description of perception about you helps to hone your thinking.
I understand where you are coming from with this line of questioning but I would be reticent to use it outside of people I know very well. As emotionally charged as this topic can become I would be wary of a stranger who already views me as infidel, sinner or agent of satan becoming emotionally wound up. In an online setting or with someone I know I can see the value.
Okay, we all can play here:
If their logic got any more circular, I'd be dizzy from it. And you're absolutely right: these people so identify with their belief system that to criticize it is to criticize them. Most of them haven't the capacity to look at their own belief objectively.
This is where the techniques which Peter Boghossian has developed may be very useful.