Yitayningwut, yes, I agree that Rambam is astounding, but it is hard to refute, since he is quite clear that there is a difference in halacha between a Tzeduki and an Apikorus. It is even more surprising that such a shechita could be kosher since the 5 halachos of shechita come from Torah Sheb’al Peh to begin with (Shehiyah, Drasah, Chalada, Hagramah v’Ikur).
As far as your point that the shechita of a nochri is pasul only because of a gezeira that he may have a machshava for avoda zara, that is correct and surprising, as well. Normally a nochri cannot do any mitzva for us. He can’t read megilla, etc. Not because of a fear of avoda zara, but simply because he is not a ben bris, or not btoras. Why does the Rambam say that he is only pasul for shechita because of a gezeira, and not midoraisa, like just about every other mitzva. I wanted to suggest that shechita may not be a chalos, but simply a metzius. If the animal is shechted the proper way, then that is all we care about. Nevertheless, that is also difficult, since we need koach adam, and a waterwheel with a knife is not normally OK (unless the person started the wheel with his koach and it shechted on the first revolution).