"if this was true, then the CERN data might have been true at that moment of the experiment"
It might have been, but since it was later found that the experiment had forgotten to account properly for the length of a particular wire, marginally less likely!
I know that Occam's razor isn't very popular around here, but that's only because it's often misunderstood. It's best seen as a guide to what you should start by looking at: the simpler explanations are not necessarily the correct ones, but they are certainly far easier to test, and then confirm or rule out as needed. In this case it is also useful: a model that claims, in essence, that constants vary in a completely unpredictable and irreplicable way, is by definition unfalsifiable. At least the "dogma" of insisting that scientific laws are the same everywhere has the advantage that it can be tested. So far, it has stood up to that test far more robustly than Sheldrake claims.
It is, incidentally, also worth noting that it's possible to put the statement "laws of nature are the same throughout the universe" on a fairly solid mathematical footing. It is, then, not just a dogma stated in words, but also a guide to what equations should look like, and what predictions they can therefore make. Again, it stands up to reasoned scrutiny.