I would say the Easter Eggers. I have yet to see one of my NH, RIR, Rocks or Sexlinks go broody. Leghorns aren't supposed to either. You don't have a real good list of breeds for broodiness. If you want to have setters, get yourself a standard cochin. Now those are broodies!
It doesn't matter if you keep the rooster in with the hens unless you don't want chicks, which to be honest, you aren't likely to get anyway because those breeds won't set. You will probably have to incubate for chicks. The hens will dilute the blue color so you could get some brown or olive color layers from the next generation out of the crosses from the brown layers. The white layer will produce white or lighter blue layers.
If the rooster is "bothering" the hens and you don't want chicks, I would remove him. Sometimes egg production can go down if the rooster is too aggressive with the hens.
