In other words, people will only convert for precisely the wrong reasons.

Absolutely true. If they were ready to accept the correct arguments, they would have become atheist on their own.

The probability for a given person to have developed a skeptical mind, have overcome the possible brainwashing effect of a religious education and all the possible correlated biases/fallacies (sunk-cost, belief-in-belief, etc.) and not having heard a compelling anti-religious argument is very low. Therefore, you can convert them either following the long, hard, but certainly more rewarding path of making them skeptical, if not rational, or you can bombard them with emotional nukes to demolish the emotional concrete walls that protect the religious belief.