The Dorchester Vase
(media.communities.win)
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Your primary link will be setterfield.org, Barry Setterfield, full but not that easy to navigate. The thesis is CDK (lightspeed decay), placing all carbon dates within less than 10,000 years. This helps with some of these concerns though it doesn't solve everything.
Briefly, OP requires a theory of sudden Precambrian formation within human memory, which leads YECs to cry deluge, although that too is a harder fit because you need something suitably molten. So I honestly don't have a prima facie theory on this one because I don't remember the volcanism effects.
Polonium radiohaloes found in Precambrian rock are very inexplicable and very worthy of greater recognition, but they arise from a formation period rather than a human period so they don't help with this vase either.
Antikythera is "out of place" in the sense of stretching our knowledge of lost arts; I'm partial to the lightbulbs depicted in the pyramid carvings myself, as we've proven they could make batteries. You also remind me of the abacus-like Ishango bone, which shows an earlier appreciation for computation than believed, and the Paluxy footprints of humans and dinosaurs frolicking together. I'll come back later though.
Fossilization can also occur much more quickly than expected
True!
WP shows disappointingly at "Dorchester pot", with the OP's source in full, that the simplest explanation is just mistransmission of the finding data, providing evidence of the pot being 19th-century in origin. As I said there is not a direct YEC explanation for finding human artifacts within granite. Since Scientific American said the results were being submitted to verification we can infer any such process ended in quiet rejection. Also it's probable based on custody that the OP photo is not that of the artifact. In those days of course Scientific American could still get away with attributing the pot to Tubal-Cain! (He's the man for whom the modern Hebrew name is now "Vulcan".)
I'll plug again that it's worth reading the "Pleochroic halo" article in WP, which makes no reference to the difficulty making any mainstream explanation of the effect work, and then searching for articles on particularly the polonium halos that show the difficulty. There you have something in granite that didn't get there by simple means. But recapitulating those physics is beyond my scope today. Verbum sat.
(Add: I also see that John D. Morris, whom I greatly respect, has suggested backing off from insistence that the Paluxy tracks are necessarily human, as there is a strong battle over custody of those evidences as well and over erosional changes, so I cannot affirm this particular evidence other than to say the whole history of that discovery needs further investigation for resolution of loose ends.)