Ooh i actually looked into this a while back so i hope you don't mind me yapping :)
So the version where Odysseus drives Diomedes by the sword seems to be a mistranslation from West? I checked the actual greek fragment he cited in his book and I don't see any indication of it being Odysseus, so I'm not quite sure what's going on there? (West uses his apparent mistranslation in at least two books, but other than that I've never seen any traces of it)
I do have to say, Conon is the earliest attestation we have of the palladium heist story (having lived from 63 BCE to 14 AD), with other attestations by Pausanias (2nd cent CE) and Hesychius (5/6th cent CE), while attestations of other events attributed to the little iliad are generally older, with mentions from the 5th cent BCE onwards.
It does seem that mentions of the palladium heist are significantly younger than the others, it's a little strange to me that its never mentioned before Conon
I think Hesychius is the first to unequivocally attribute the palladium heist to the little iliad (id need to double check this tho), the summary of Conon's narrations does not reference the little iliad specifically (though obviously it concerns events from the little iliad)
So I dont think we can be entirely certain when the palladium heist story came to be. It could be a misattribution by Hesychius to attach it to the little iliad. And we can't really know where Conon got the story. He is an author known for prefering the more unusual/strange stories, which might explain why we first see the palladium heist recorded by him.
I think saying the palladium heist is fully roman/invented by Conon is a very big assumption to make, but I also don't think we can uncritically attribute it to the little iliad. It might be a later story, it might not be, ultimately, I don't think we'll ever really know when exactly this myth started circulating and how much it was or was not a part of any hypothetical canon epic cycle
That said I am definitely not trying to argue with the point you made in your original post because I fully agree. I think people's eagerness to take the palladium heist as purely a figment of Conon's imagination is very revealing of this Greek/roman dichotomy and the 'our good, pure greek myths and their stupid, barbaric roman myths' thought process thats apparently going round lately