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
I'm looking at Delawares. I like so many things about the breed ... dual purpose ... fast-ish growing ... big ... good winter layers of big eggs ... broody enough ... eager foragers ... smart ... sweet ... and pretty (though that last thing doesn't matter so much to me). Delaware is a heritage breed, and it is in need of restorative breeding. I know zilch about breeding, but am hoping to work with someone else who does.
With a true Dual Purpose breed I don't really need to run different flocks. I'd have a breeder setup for sure, but the hens in my main egg production flock could brood and raise the chicks, then the cockerels would be put in a grow-out pen when they become jerky, and the pullets would stay with the egg layers unless they are selected for breeding. Sounds "simple," so I hope it is!
There are a lot of interesting alternatives to the Cornish Cross available ... (but it bears repeating that raising the few Cornish Cross that I raised was just about the easiest chicken experience I've had, and the results were HUGE and DELICIOUS!)