This is coming to an end.
My parents will be back next Monday. Not quite sure when Nemo and Itsy will leave, but it should be early next week.
Although it's been a rough beginning, things did settle.
The extra room did help as well; if one of them, most of the time either Nemo, Itsy or Zuri, would get too restless towards another bird they ended up in the bird room for a little independent play. It kept things going smoothly.
This has also showed me that my flock is somewhat receptive to new birds; Zuri was only going after Itsy, never Nemo, and she didn't chase Itsy all the time so if I am to add a Red-bellied and not another Meyer's, maybe she won't have any reaction at all. Shade stopped early on trying to get Nemo and she was always fine with any of my other birds. The others didn't really seem to have noticed that there were two new birds to deal with. Good experience overall.