You folks have the issue that all of the 999 timelines seem to start in the same place. And that'd make sense were it not for the content of the bad endings and the fact that the game was made in the first place (the girl has to die somewhere).

999 originally had the following shaped flow chart where K is Kanny (D is dies and L is lives), 5 marks the start of the game and T marks the true ending (S is safe and A are other bad endings condensed into one arm for simplicity):

KL——5——T

There are no bad endings. Kanny always lives. That's the only past available.

Your trident looks like this.

............/——S
KL——5——T
............\——A

It's inaccurate to say the timelines split in Junpei's escape room, naturally. That's just there for simplicity. Anyway, that looks good, right? All paths stem from a path where Kanny lives. Except that's impossible...the S path cannot happen if KL is in its past because in that world the T was not reached. The point of the game is that Junpei and Kanny had a connection. Junpei led Kanny to death four times as a result of the theory, and she did not try and goad him into the true end path.

Moving on, the actual model must, therefore, look like this:

KD——5——S
KL——5——T
KD——5——A

The future and the past are inextricably linked. You cannot disconnect the two and get a trident for the sake of the future making sense. The bad ends must involve Kanny dying in the past. S and A Junpeis did not give Kanny a solution though the field, and she died. This also helps resolve the issue of why the game happened without an original timeline. The girl died in several worlds as she was supposed to.

The issue you may have now is that the 5s should all be the same 5. That might be accurate, and, given the mess the game is in, we can't really account for how Kanny's death led to Santa making the game with or without June not involving an original timeline. We'll use the following model for everyone's sanity:

K?——5——?

Does Kanny live or die? Which ending do we get? Junpei's door choices decide. However, after crossing the point of no return, it becomes evident that either the girl dies or will live. Recall fevers. The figure collapses to the following:

KD——5——S
KL——5——T
KD——5——A

In other words, Kanny experiences a fever in the boiler room because they are already on the top row world of the flow chart approaching the safe ending. Kanny dies in the past--as a result of what is to come--so the past manifests itself in the future. June won't last long. And if we did have a trident, there is no way to account for the fevers because she doesn't actually die in the past.

I'm not touching on how Kanny can exist because she can't. The KL timeline can't exist without the game, and, if she died, the game can't exist. This system can't exist. The explanation the writer will probably use is that June body jumps upon death both in the safe ending (which we observe) and in the incinerator. This trivializes everything because, then, the girl never dies meaning the game never needs to happen at all if she has the power to go to another world to cheat death.