Beast, observational studies are (1) of limited scientific value and (2) cannot form part of a rigorous scientific review of the evidence. And (3) whether they are biased is determined by their actions, not their descriptions of their pure intentions. Finally (4) if I am right, it is a reason to avoid all meat from stunned animals - exactly the opposite conclusion you've drawn.
(1) If you want to confirm that a stun has rendered an animal insensate, you have to do something other than observe. Observation can confirm lack of movement and can tell you about error rates in the stunning and slaughtering processes, but they can't tell you whether the animal is feeling pain. In fact, paralysis makes it particularly difficult to tell if an animal is insensate, as the animal's body movements cannot be observed (like humans, animals will flinch away from pain sources, for example - but they can't if they're paralysed). To test for pain in animals requires physiological studies, plus imaging studies of nociception. It's not easy to do, which is why people resort to shortcuts of saying "the animal is not moving and its eyes are closed, hence it is insensate".
(2) a new observational study of UK slaughter for one week is by definition new scientific evidence, and does not form part of a review of the current evidence. A review would identify all relevant studies and then weight each study on the basis of the rigour of the methods and analyses in a meta-analysis, to see whether a sufficiently clear picture emerges. The Cochrane Collaboration does this for medicine. I don't believe there's any analogous effort for animal slaughter.
(3) science is not just about rooting out overt bias, but unconscious bias. I am sure that the RSPCA hold a genuine belief that they are not predisposed to either back or work against religious slaughter and are simply working from the evidence, but that does not mean they do not hold such a bias. It may just be well hidden from their view. I personally think there is a quite plausible chain of reasoning by which one could expect bias to creep in (I mean, modern stunning via captive bolt must surely sound more inherently likely to be less painful than a slaughter method developed by religious groups hundreds of years ago). And thus, I think there is all the more reason for the RSPCA to be extra careful about bias, which makes me worry when they say "we're not biased" because that suggests complacency.
(4) if I'm right, then meat from stunned animals may be less humane than shocheted meat. So I don't understand why you conclude that you would eat only the former. The logic doesn't follow.