I've never been in this situation and I can't imagine what you're going through.

But when I have positions that get challenged by a lot of people, I have had some success in writing very long and complete essays detailing why I hold the position, along with all of the responses I expect to get and why they're wrong, and putting it on a blog or website. Then when someone asks why I believe X, I just tell them I'll send them a link to the essay. It weeds out the people who don't care enough to go to a link, and it lets the people who really want to know see the position defended as best I can without having to come up with it on the fly. If there's any pre-existing explanation of atheism you really identify with, you could use that too.

And I have had good experiences with religious people by confounding as many atheist stereotypes as possible: being exaggeratedly nice and understanding, mentioning how much I enjoy religious music / religious writing / the teachings of Jesus / whatever else I honestly respect about religion but saying that some other parts aren't for me, not bringing the issue up but having a few overwhelmingly strong points that they will agree with when it is brought up, and having a link to a more complete argument ready in case I feel a discussion is getting too confrontational and counterproductive.

I also find that if my goal is just to end an argument without losing too much social capital or coming across as confrontational, I get better results with emotional rather than intellectual points, as long as the emotional points are framed in a nonconfrontational and nonchallenging way. Going on about Biblical contradictions just gets a "You're obviously proud of your worldly learning, but worldly learning leads you astray" or something from the less intellectual, and an attempt to rationalize the contradiction from the more intellectual. But if I say that some of my Jewish relatives died in the Holocaust and I don't accept that a just God would allow that to happen, most people have the social graces not to go into a full-fledged explanation of proposed solutions to the problem of evil and to just let the matter rest, or to say that they think my heart is in the right place and they'll pray for me or something, which is really the best one can expect in these sorts of situations.