Have you looked into the Sagitta? I don't know if it's considered a true breed yet; it's a hybrid that is supposed to breed true and is feather sexable - - RIR/NH/Cx. They are red with black and/or white highlights. My pullet is red with black in her tail like a RIR, but rounder, fuller body, and definitely is going to be a good sized hen. They were specifically created to be dual purpose - the high egg laying of the two red breeds with faster growth and larger size due to the Cornish cross influence (they don't grow fast like a Cx, but a bit faster than dual purpose breeds). I don't know where you can get them from source, mine came from a feed store where there were only pullets.
She tried to go broody when the eggs piled up in the nest while I was gone for a week, but after three days of me taking her our of the nest a couple times a day, she gave up. So they can go broody, at least if there are enough eggs to make a clutch, but are easy enough to break the broodiness if you want to. Mine is very food motivated, one of the tamer girls I have; she will eat out of my hand.
I realize some breed folks will probably turn their noses at a hybrid, but that's what most breeds really are anyway - hybrids that breed true.
Here's a link to a pdf from the company that created them - it looks like it's geared toward hatcheries that are going to raise chicks to be parentstock to lay and/or hatch eggs.
PARENT-STOCK - Centurion Poultry, Inc.
www.centurionpoultry.com/default/download_pdf/53