Those ideas sound interesting, I was also thinking of changing power weapons for chainaxes and whatnot, but they would still be power weapons.
I like the that certain Carcharodons were chosen to teach them the chapters history and lore, that way they speak the ancient High Gothic, the geneseed will be the same so they'll have the same flaws.
Another idea aswell is that instead of serving with Guilliman's Unnumbered Sons, they were dispatched on their own to do what Carcharodons do and perhaps not many, or any, other chapters knew of these Carcharodons.
It's have a 'New Dog, Old Tricks' feel, as backwards as that is

Chain weapons and markings will be in though.
An alternative idea is that it's a separate chapter made from Carcharodon gene-seed made with the supervision of the Carcharodons?