I really like this theory, though I find it hard to believe kaneki will go through even more changes. like.. hes come full-circle right now, he seems resolved and alright now.

This is the first I heard of the theory so this is a bit off the top of my head, but it depends on how you look at major changes. First, we might be able to ignore Urie for now. He might be Kaneki's opposite. Each of the deaths have also affected Urie greatly as well. So the last major "change" might involve Kaneki killing or being killed by Urie.

• Shirazu was reluctant to accept what he was, and that ghouls could be people - Represented Kaneki was he first was - Death was Haise accepting Kaneki.
• Mutsuki battled with what she was born as and what he was now. - Basically Kaneki between accepting what he was up to his torture - Death was Kaneki accepting that he should quit looking for "suicide by X" and actually live. That he should quit trying to take the easy path.
• Saiko has a very powerful ability that seems hard to control based on how rarely she uses it, and the damage it causes - She's likely Kaneki as Centipede
• Urie... I don't know. He's changing so much to get a peg on yet.

So it looks like the first Quinx represent Kaneki's becoming at least Centipede to a degree. So the next logical step would be that Urie might become the next "Haise". That if Mutsuki is dead that between his death and Kaneki turning "traitor" that Urie might be inspired to become the weapon CCG wanted Kaneki to have become.

Since the deaths of the Quinx seem to parallel Kaneki accepting something about himself or his circumstance. Either Saiko or Urie will likely die when Kaneki accepts his role as a One Eyed King. Though I'm leaning Urie. If Urie is being built up as the anti-Kaneki, the Haise that was Wanted, then the current OEK is going to fall. It'll likely end up being Kaneki vs Urie for the title of OEK. Assuming there isn't going to be two at once in chess symbolism.

So the question is what between now and OEKness could Kaneki accept that would mean Saiko's death? Since :Re has so many parallels to TG, my hunch for now is at some point there will be a "Kaneki returns to Anteiku" parallel where he decides to end being Centipede devourer of ghouls, and try to have a normal life. Only we all know how that turned out. Instead it may be an attempt at an olive branch that ends horribly forcing a battle/war to happen with Kaneki accepting there is no peaceful way things could change.