As far as I am aware, the only approach used by Jewish groups to defend shechitah is to argue that it is painless. I don't know if that is true or not. (Some of the "scientific" defense of shechitah seems rather dated and biased. On the other hand, I have seen various quotes from Temple Grandin saying that shechitah can be done without undue pain, and that the main issue is how the animal is treated beforehand.)
But what I do feel is that an alternative strategy should be considered. Because I know of no theological reason why shechitah should necessarily be entirely painless. Furthermore, if you defend shechitah on the grounds that it has "scientifically" been proven painless, then you are effectively conceding that if science proves otherwise, then shechitah should not be done.
Instead, I think that shechitah should be defended on the following grounds: that to the extent that pain is caused to the animal, this is justified for religious benefits.
No country rules that no pain may be caused to animals. All legal systems allow pain to be caused to animals for human benefit. Medical experimentation is one example. Even farming animals for food usually involves some level of distress to the animals. Yet it is permitted, because people are entitled to eat meat.
Of course, this is not unlimited. The pain caused to animals must be commensurate with the human benefit. Many countries prohibit various blood sports in which the pain caused to the animal is not considered justified by the pleasure of hunting. But when there is substantial, legitimate benefit to humans, all legal systems permit causing pain to animals.
Shechitah is the only means by which Jews can eat meat. Eating meat is a legitimate human need, and Judaism is an ancient way of life which deserves respect. Even if shechitah does cause pain to animals, it is justified - especially since the suffering is likely not of long duration. I think that this is ultimately the correct defense (although I will admit that I am not certain if, strategically speaking, it is the best defense to use).
At the same time, the kosher meat industry certainly could improve a lot in terms of how the animals are treated before shechitah. I'm always amazed at how people who are makpid about every minutiae of rabbinic chumra are often entirely unconcerned with the d'Oraisa of tzaar baalei chaim. As Rabbi Aryeh Carmell ztz"l wrote:
It seems doubtful… whether the Torah would sanction “factory farming,” which treats animals as machines, with apparent insensitivity to their natural needs and instincts. (Masterplan, p. 69)
Many halachic authorities are of the opinion that minor benefits and financial benefits, such as those obtained via factory farming, do not warrant causing pain to animals. It is true that the majority opinion is in the other direction. Still, considering that many people are fastidious to meticulously fulfill the laws of kashrus according to all opinions, such punctiliousness should surely also apply to the laws of tzaar baalei chayim. That is to say, since there are opinions which state that financial benefits (such as those enabled through factory farming) do not justify the suffering thereby caused to animals, those who are meticulous to follow all opinions should surely be consistent and refrain from consuming animals farmed in such a manner. Additionally, they should be working to ensure that farmed animals suffer as little as possible, whether they are farmed for food or fur. Aside from the innate importance and value of that, I'm sure it would assist in the general campaign to defend shechitah.