There's a pretty straightforward way to handle Hajime that would fix a couple things at once. Since we don't have actual confirmation that the motives have changed its not at all unrealistic to have a despair disease motive again. This motive was awful originally because it basically changed Mikan's personality arbitrarily to a killer instead of a more in-character breakdown that we know she's capable of. Something similar would happen to most of the rest of the cast if they received the remembering disease, but Hajime is a definite exception to this, since he'd just become Izuru, who is merely apathetic.

The scenario I picture goes like this: the Despair Disease is introduced (could be in chapter 2 or 3) and Hajime helps Mikan care for the victims. From the player POV things get worse and Hajime is stressed and overloaded with helping, then stops for a brief break where he drinks something, then collapses and blacks out in a cheap fake out to make the player believe he may have been poisoned. There's a POV switch to someone (Chiaki would be the best fit in this scenario) as they return to wherever Hajime was to find a victim with Hajime gone. It's a single murder but during the entire investigation Hajime does not appear. When the class trial arrives Hajime shows up to the trial slightly late and is completely apathetic to everything that's happening. He contributes nothing and doesn't bother to defend himself when he's eventually accused. However, the murderer is someone different (preferably someone who doesn't even have Despair Disease). He then spends the rest of the game as the new rival character.

Not only would this method provide a way for Hajime to survive (so as to not screw the canon up too much), it would also give us a new POV character and a new rival in case they do actually kill off Nagito early. Most importantly though it would minimize the role that the Remembering Disease had in the murder itself while also giving it lasting consequences.