I agree the bird you're looking for is probably a Dark Cornish. They're good foragers, good broody mommas, and nice meaty birds.
That said, here's free advice/thoughts generated from your post. You didn't ask, but here ya go anyway........
I think you're going to need an incubator.
Or some large Cochins, something like that, another breed that's more devoted to going broody.
Most broody hens are going to give you 2 clutches a year. Some more dedicated birds might go three, like the silkies, Cochins, game birds, etc. But keep in mind each clutch, from when she starts setting to when she weans the chick around 6 weeks, takes 2 months. Then, you have some recovery time for the hen. It's not healthy for her to go broody back to back, she needs to regain some condition and start laying again. So count on 3 months from the start of one clutch to the earliest when you'll start the second clutch from the same hen. Most birds will only brood in the spring or summer, there are rare birds who brood in the fall but it's more hit and miss from the individual bird than a breed.
Logistics of housing that many broody hens raising chicks.....I'm a big proponent of a broody raising chicks in the flock. But, having multiple broodies at the same time can complicate things. Hens get confused, or they see other chicks as threats to theirs, and things can get nasty. So, are you housing each broody and her chicks separate? Or just 2 broodies per pen, with different age chicks? I don't see having say 4 brooding hens in the same pen unless it's a very, very large pen. Or you have an option to free range, that would help everyone get along.
If you have an incubator, you can set say 100 eggs and have one hatch to deal with. Brood and grow those chicks out in one batch. You can stagger your butcher dates, cockerels first, then let the pullets grow out a bit longer as time allows.
Logistics of housing that many birds to grow out. These aren't the CX that get processed at 8 weeks. You'll need housing for all these growing cockerels and pullets until they're around 16 weeks. That's a lot of space, to keep them from pecking each other and generally driving each other crazy.
You didn't mention previous chicken or meat bird experience. Have you eaten non CX birds? They're a bit different, and a lot of folks like the idea of them far more than the reality. Kind of like grass fed beef.
My advice (again, free and unsolicited, take it for what you will) is to start smaller. Spend 2017 trying a few different breeds. See how you like them, how well they work for you. If you're only after meat, you might not be opposed to cross breeding. Start with maybe some Cornish, some good Rocks, Delaware, Wyandotte, something like that. You may wind up with say a really nice Rock hen who raises 3 clutches a year and is heftier than her counterparts.....put her under a Cornish rooster and hatch every single egg she lays. Keep those pullets as future broody mommas and butcher the boys for the table. This is just an example, I'm trying to say experiment a bit and find individual birds that fit your needs, hang on to them and reproduce them like crazy!