Well the stuff about Oars actually having pulled land is a neat idea (and that some spoilers for tomorrow's chapter mention Pangeae is almost a spooky coincidence, or not?), but in the end even if this is true, I'm more inclined to believe this is just something that once happened in the rich history of the OP world and doesn't have any real relevance to the story's plot.
I mean I think people are going to notice when the world goes from a single continent to an archipelago-like geography. With other words it can't be something that they tried to hide, in particular because they gave him the epithet "land-pulling". And despite his size and strength, I really can't imagine him alone going to move all the landmass in the world.
A more plausible scenario would be, at least for me, that Oars was enslaved/captured or something along those lines and ordered by a Celestial Dragon to pull land for whatever reason till he drops dead. Similarly to how they once ordered a bridge to be build in East Blue centuries ago to nowhere. After all he supposedly died 500 years ago, so whatever he was involved in, it happened in the 'modern era'.
And in regards to that cross-symbol, yes it's striking that it appears on that wall, but even if it's intentional, I really don't think it's that special. There are actually a few other instances in the Thriller Bark arc where similar symbols appear, in line of the overall theme of that arc (vampires, zombies etc.), so Moria might have made Oars wear that short. And/or it might also be some kind of unofficial symbol that joins the logos of the WG (a cross with 5 dots) and the Marines (seagull wings stylized into an M). I wonder that if you would read the entire series and search specifically for that symbol, you might come across it several times.
The stuff about the strawhat and the freezing though seem irrelevant. Cold simply preserves. The reason Oars was being held in a fridge, was to avoid his body decaying and the reason it got preserved so long, was because he died in the cold and maybe they put that strawhat in the freezer thinking it would preserve it better. Oars Jr's hat was made by Ace, which he learned in Wano, so I don't see either any real significance behind this either.