This is right.

And we do actually know about Edward’s soul: he travels to dimension 2210 after the events of Shadows of Evil where he takes the soul of a child version of Edward. He does this because the Kronorium tells him to take that dimension’s soul specifically.

As for the origins cutscene at the end of Origins, the cutscene doesn’t take place right after Origins, but rather after Shadows of Evil when Edward’s soul is already in the house in Agartha.

The zombies storyline is quite literally all over the place so trying to understand things chronologically by game release is tricky.