There is a thread on the forum about people trying to do that with Freedom Rangers. That's another type of broiler bred to grow slower and be better at foraging. That thread went on for a long time as people reported their results. The message I got from it was that they were real hard to keep alive and to a weight they could breed. Like the Cornish X you would have to restrict their feeding to be very successful.
Basically any of the Dual Purpose breeds will do what you want. That's why the Dual Purpose breeds were developed. Before the Cornish X was developed, certain Dual Purpose breeds were used for the broiler market, mainly the Delaware, New Hampshire, and White Rock. These were strains of these breeds that were specially bred to produce meat more than eggs, but still lay OK.
They are not the same as the Delaware, New Hampshire, or White Rock you get today from the hatcheries and not from a lot of breeders. With chicken genetics, if you don't reinforce specific traits every generation by carefully selecting your breeders, these specific traits get lost in just a generation or two. The traits I am talking about are body size and feed to meat conversion, basically how fast they grow on a certain amount of feed.
The reason these breeds were chosen to develop as meat chickens was their light color. When you pluck a chicken, you leave some pin feathers behind. You really have to be diligent to get all of them and it extends processing time quite a bit. With dark feathered birds these pin feathers are easy to see. With the lighter colored birds, they are still there but you cannot see them. You get a prettier carcass with the lighter colored birds if you pluck and you cut down on your processing time trying to get them off. If you skin it does not matter.
Each hatchery and each breeder is different, but in general the hatcheries goals are not to produce birds of these breeds that are great meat birds. That's what the Cornish X is for. Their goals and breeding methods are more geared toward mass producing a chicken that in general meets the goals of a backyard flock. They mainly look about like what the breed is supposed to look like but they are not worried about size and feed to meat conversion. With them, it is more about eggs and general colors and patterns. They are not into breeding grand champion prize winning show chickens and the prices they charge reflect that.
The breeders are where you are possibly going to find something closer to what you want, but you have to use caution. Not all breeders have the same goals and not all breeders have equal ability. To get what you want, you need to find a breeder that is breeding for the traits you want. Some breeders are breeding to produce a grand champion prize chicken. They use special breeding techniques to try to breed that perfect chicken. These chickens will be larger than the hatchery chickens if the breeder knows what they are doing, and you will get chickens that have good body conformation, which means more meat on the body. But many of these are more worried about leg color or how many points on the comb and how the comb looks than feed to meat conversion. Egg production is not a goal either. In some cases, good egg production actually hurts a show chicken.
There are some breeders trying to recreate the original heritage chickens with the rate of growth as well as the other original traits of the heritage breed. With the Delaware and New Hampshire especially, feed to meat conversion was a heritage trait, but it is not judged in shows. Any breeder that incorporates heritage traits like this in their breeding program has to work harder to win that grand prize. But some do.
I went through all that to point out that you can't just look at breed. You have to look at the strain of the breed, what specific traits are the breeding flock being selected for. To get strains that are bred specifically to do what you want may be expensive. The breeders that develop these chickens put in a tremendous amount of work and go to pretty high expense to develop them. And even the best breeders reject a very high percent of their chicks as not up to standard. But their rejects are almost always better than hatchery chicks as far as meeting specific goals. You don't go to a plow horse farm and expect to find a Kentucky Derby winner. You go to a thoroughbred breeder to get a fast horse, and even then not all will win the Derby.
I do think if you start with good stock, which will come from a breeder that is breeding to meet your goals, you have a huge head start on developing your own specific strain to meet your goals. Even if they are not breeding for all your goals but only some, you will have a better head start on getting where you want to go. But whether you maintain that advantage is up to you. Remember, I said if specific traits are not reinforced each generation, they quickly go away. Even with good stock to start, you have to select your breeders with care to maintain or improve the traits you want. In a self-sustaining meat flock like you seem to want, that means eating your small ones and breeding your large ones, as well as selecting for body conformation, personality, egg laying, or any other traits that might mean something to you. You also have to watch for lost fertility or inherited defects. To develop your strain like you want, you will have to do a lot of inbreeding. Inbreeding is how good breeders develop what they want, but you do have to be on the lookout for traits showing up that you do not want.
You can do what you want from hatchery stock. That's how I am going about meeting what I think are your general goals. But it will take a few extra generations to get where I ultimately want to get. My better roosters are pretty good size after just a few generations, but I still get a lot more of the smaller ones than my ultimate goal.
I've probably made it sound more complicated than it has to be. We are all different and have different goals, set-ups, and management techniques. If you mainly free range so you are not buying a lot of the feed, food to meat conversion ratio may not be that important to you. If you want to butcher tham all at one time as opposed to just doing a few as you go along, you'll have different desires than me. We are all different. I usually wait until they are 15 weeks old or older to butcher. I don't fry or grill mine but use slower, longer, moister cooking techniques.
Good luck on your project.