It seems I have to re-evaluate my understanding on something: While parallel incarnations are a thing, and some of them do work in the manner of sending a soul shard which works as a "bot" on the other incarnation, it is also fully possible to have parallel first person view incarnations if they are in separate timelines. That means they are performed with no causal influence to each other during their play-out.

The topic was touched on in Zhuan Falun with the example of a buddhist monk who goes to meditate, sits down and then he goes into deep trance in the temple. His souls leaves his body and re-incarnates someplace else, because the temple life isn't suitable for removing his karma and showing him what he needs to learn. So he starts over in a direct parallel incarnation and becomes enlightened over there, then "ascends" from the other life. His soul then returns to the body in trance, which has been sitting in the temple hall for 50 years, and he now has all this knowledge from the life he lived in a different location. (This would be possible during the very stable empires of the past when nothing changed for 100s of years.) To the other monks at the temple, he just meditated for a very long time, they can't know he actually lived somewhere else and came back.

I just don't recall in this mental framework which of the past "parallels" were first person view or not, unless I adapt completely to that (from this view) very narrow mindset of the past. What takes place in the "past" makes no impact on time progression in this timeline, and memories when they do surface, will appear in a chronological orders, giving an impression of "parallel" existence of a different mind. I guess I was more successful in these operations than I could understand from within my current mentality. And that's a serious understatement going by what I learned just about this life as I recently backtracked events and what effect they had on the world around me, like the economic crisis in the 90s and other things. Oh well.