We know about Chief Mountain in Montana, where "older" rocks overlay "younger" rocks. We know about Scotland's Knockan Crag, with schist over limestone, and Ben More Assynt, with quartzite over sandstone

Well, I didn't, so thank you for bringing an interesting snippet of information to my attention.

This is at the heart of science and the biggest single difference between it and a religious belief. Scientists know that even when it explains all the facts it is likely that any theory it has is oversimplified. When new data that doesn't fit is discovered, a minor adaption may be all that is required. In others, a significant adaption may required, and in some cases the whole shooting match needs to be dumped (eg 'phlogiston theory', 'the ether') but let me stress the obvious: in each case the original theory is falsified.

Now, your claim is that AEN 'approaches unfalsifiability' which is a pretty hard phrase to interpret. The only meaning I can assign is that you agree it is falsifiable, but the evidence required to falsify it would have to be very substantial. I'd agree with that. If, on the other had you mean it does not 'approach' unfalsifiability but actually is unfalsifiable, I'd beg to differ. If, for example, we discovered a way to take non-radioactive elements and create an artificial stone in the lab that mirrored the carbon dating results of a 'real' stone that we were modelling, then all evidence based on radioactive dating would be suspect.