I think it's safe to say Levaszk had nothing to do with III's death, rather he just took advantage of it. He has not once in the campaign demonstrate an ability to command others, not on the same level as Maya pulling one of the Nine into 3D space. The loretab for Giver's Blessing shows him taking control of a Dreg to kill a heretic, but that's about it.
I think it would be best to keep the section as it currently is as Maya being responsible for III's original death and us seeing a flashback just makes sense, and seems to be what the general consensus in the community is, and feels less complicated than us reviving III, who then dips back into the Nine's dimension only for Maya to pull them back a few seconds later. Its second death can easily be explained that, though the Haul revived, the Nine still can't exist in a 3D space.
Plus, I recall one line from Message from Maya where she pretty much said her business on Kepler was done, which almost certainly means III, unless she just decided to return to kill it again for some reason.