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I think the Mormons are focusing on the Evangelicals because they know the press hates Evangelicals, and also because people who leave Mormonism would most likely go to Evangelical Protestantism because this was one of the streams in its formation (that is, Smith drew upon things that were around him, which included everything from born again Christianity to spiritualism to looking for treasure through a crystal in the bottom of his hat...).

Why do you suppose that Mormons would become Evangelical rather than Catholic? Mormons have a lot of common ground on many issues that other denominations don't. The stress that the Catholic Church puts on a priesthood hierarchy is very similar (though the authority that the pope claims to hold is a bit more limited and very different in nature than the LDS prophet claims since Mormons can issue new revelations.)

LeGrande Richards, a long deceased Mormon Apostle, even comes to the conclusion that only the Mormons or the Catholics could be true. His reasoning is that Apostolic Succession of the priesthood by the laying on of hands is necessary. Therefore, either Jesus' Church was always on the earth (and would thus be the Catholic Church), or it apostatized and needed to be restored (which would make the Mormons true.) His argument is that the "protestants" came out of the Catholic Church and therefore couldn't be the original Church.

However, if a person leaves Mormonism, then the denomination a Mormon chooses will also depend on the reasons they are leaving. If the Church has overworked them and worn them out with mountains of priesthood assignments, they may opt for a less works oriented faith of the "once saved always saved variety" but if they accept most of the LDS Church's emphasis on priesthood authority and ordinances, they are very likely to be more Catholic in their tendencies.

BTW, I think the reason that LDS Church is focusing on Evangelicals is because Evangelicals are the ones most passionately and vocally opposed to Mormonism. Many Evangelicals wouldn't vote for Romney no matter what because of his Mormonism...which is how the Republicans ended up with McCain instead. The evangelicals went to Huckabee instead. If not for that, Romney would have been the Republican nominee instead of McCain. The Church has noted this. Besides, Evangelicals are also one of the largest Christians demographics in the US too. If the LDS Church is ever going to be accepted as Christian in the US, it's got to win them over with PR. Just a few of many thoughts to consider, I guess.