My speckled sussex are great broodies & wonderful layers and they get along very well in my flock (which includes barred rocks). When I do let them hatch out chicks they are excellent mothers. I'll warn you though, once they set they expect chicks!
My first choice for your criteria would be the Sussex. Lots of people on here post about how great the Orpingtons are at being broody and great mothers. I'm sure there are others.
Olde English Game Hen females are tremendous mothers and I think they get along with your other breeds. Not sure about their egg laying. The Olde English roosters, however, do not get along with other roosters and will probably fight to the death.
Silkies and Buff Orps! Last year I had a silkie mix hatch 3 batches of babies! she would sit, hatch, and raise them for about 6 weeks, then star all over immediately! This same hen started sitting 2 months ago and has a nice brood! And I have a Buff EE Silkie mix sitting right now! My Silkies and Silkie mixes are amazing sitters and mamas!