Sorry to hear BEHRly paint at all was your choice but you are stuck with it now. Make sure to work from wet to dry. I would stick with a 9" cover as you are going to be fighting sags and drips with your paint choice. Get a good, sturdy extension pole for the roller.
As for flat over the eggshell or satin. It should work out fine. Best if you get the flat on within the recommended recoat time or after 30 days when the surface has cured. Not critical though.
Do rescue your project with real paint from a paint store if you decide to switch to flat for you final coat.