My unsolicited take is:
First, we need to establish the concept that time doesn't "line up" across all realities in the same way. C&A mentioned this in the episode, but it's been missing from the discussion thus far. Say I have Nightmist open up a portal to several realities, all at the same moment by my clock. One might open on a reality in 1726. Another might open on a reality in the year 3000. Still another might open during the ice age. I think, if I guess correctly, that if Nightmist closes those three portals, waits ten minutes by my clock, and then opens the same portals to the same realities, you get a portal to 1726 + 10 mins, one to 3000 + 10 mins, and one to ice age + 10 mins. Time progresses at the same rate in each reality, but their starting points aren't the same. Fundamentally, this is how characters accomplish time travel: they don't jump "back" or "forward" in the same reality, but instead they jump "across" to a different reality that is in the time they want.
An immediate point that follows is that not every reality has a Haka. Why? Because in some, it's the year 1086, and Aata hasn't been born yet.
At some point, the mysterious I'm-totally-on-board-with-the-Maria-Helena-theory entity becomes aware of OblivAeon, decides that they need Haka around, and Does the Thing that binds Aata (in the Core Game timeline) and Arataki (in some obscure other timeline) together. They become immortal, and start to absorb power from other Hakas (who I won't refer to by name) in other realities. This happens at the time in the Core Game timeline when Aata wakes up to find his Ta Moko gone. Either that was the time where the Core Game timeline was when La Entitydora fought OblivAeon - since the timelines don't all line up - or La Capentity was able to go back into the Core Game timeline to that point because she's one of the only characters with that capability.
Hakas begin to absorb other Hakas. My guess for the mechanism is that when Hakas die, their power goes into other realities. This explains why Aata and Arataki gain power slowly (and constantly) over time: because the timelines don't all line up, different other-universe Hakas die at different times as seen from the Core Game timeline. Each time one dies, from natural or other causes, Aata and/or Arataki gain power. With so many alternate Hakas to absorb, this appears to be a constant, steady gain in power.
Eventually, the OblivAeon fight happens in the Core Game timeline. NightMist opens the gates, and Aata goes off into other realities looking for heroes to recruit into that fight. One of those heroes happens to be Arataki, who comes into the Core Game timeline and fights OblivAeon. When, eventually, the heroes defeat OblivAeon, the mistgates close, (1) trapping Arataki in the Core Game reality which now becomes the RPG timeline, and (2) trapping Aata in the reality he happened to be searching for allies at that moment, which happens to be a very similar reality to the Core Game one and now becomes the Tactics timeline.
X-TREME Prime Wardens Haka isn't a guy we really need to worry about - awesome as he is, the TIMEVTIME cover actually includes both the X-TREME Prime Wardens' entrance into the Core Game timeline and their exit. They pop out of the portal into some other reality, to go be awesome, probably. Or maybe radical. To the max.
However, the X-TREME Prime Wardens do have a useful purpose here: they rule out the idea that (Core Game) Aata and Arataki are the only Hakas to absorb other Hakas. Because the cover says that the X-TREME Prime Wardens are "alternate reality versions of the Prime Wardens," and X-TREME Prime Wardens Haka is clearly able to fight as a member of the team. So various Hakas have been absorbing power from other realities' Hakas across all the timelines of the multiverse.
In this model, Eternal Haka is just another of those Hakas absorbing power. However, he seems to have been doing so for longer than any of the other Hakas - including Aata and Arataki, which doesn't make sense if The Thing happened at the same time (as seen from the Core Game timeline) in all realities. One possibility, though, is that Eternal Haka is the very same person as Core Game Aata, and the Final Wasteland is the end result of either the Core Game timeline (pre-OblivAeon) or the Tactics Timeline (post-OblivAeon). The Final Wasteland gets weird because Chrono-Ranger, the only other character able to travel back through the same timeline, averts the Wasteland from happening and erases Eternal Haka from existence, Marty-McFly-style. This is the point where my understanding gets most shaky and I don't think things quite line up.