Yeah, agreed, we don't see any explicit evidence of him being able to pull III into 3D space, but then again we do see the House of Exile use all sorts of technology that manipulate/use dark matter (e.g. the terminals that activate Matterspark, Relocators, Mattermorph, whatever tech allows them to refine dark matter into Ether); who's to say that the Exiles aren't capable of building a device to bring III into 3D space?
I personally think that it would be best to simply leave the cause of III's first death ambiguous- while having Maya kill III offscreen before The Message makes sense, we simply don't know if that's what happened, and until we have confirmation one way or the other, this interpretation is speculative and shouldn't be presented as though it were definitively true.
Likewise, the proposed explanation for why III's corpse disappears and reappears is also speculative; we do not know why III died a second time, and we do not know whether reviving III transported it back into higher-dimensional space, or whether it remained in 3D space and died again because it couldn't survive there. I interpreted its disappearance as signifying that it exited 3D space and therefore could no longer be seen, but honestly this is speculation as well- again, we really just do not know exactly what is happening here.
As for the message from Maya, good point- but, at the risk of sounding like a broken record, we simply do not know what exactly she meant by that. Maybe she did kill III offscreen, and then came back to kill III again on-screen at the end of the mission - both are viable interpretations.
Anyway- not trying to be annoying or confrontational with all this, but I do think we have a genuinely confusing plot element on our hands, and I think we should reflect this in the article by not over-interpreting what we're shown. However, if there's something in-game or in the lore that provides context that I'm overlooking here, please let me know :)