Rereading the manga up to this point, my theory is that Shino (black haired girl with the pixie cut who saw Hiroki doing magic) is Bart.
She could be taking a while to remember because Bart was dying of a physical wound before he was maybe ‘killed’ by magic. The other two characters who remembered late, Watanabe and Abe, BOTH were also dying from some sort of physical injury before they were finished off with magic, so maybe that complicates the reincarnation a bit?
Plus, recent chapters brought up the possibility of people reincarnating after being killed by healing magic, and it just seems like appropriate timing to reveal Bart’s been reincarnated, considering Hiroki’s reveals, wanting to see Bart again, the general increase in Bart mentions... Also I just think Shino and Bart have similar mannerisms.
Oh, and Shino has a necklace like the one Hiroki’s wearing to remember/imitate Bart.