I’m Interested in finding a way to grow out the cockerels for the best meat.
"Best" is a subjective term. It means different things to different people. What traits make a good meat bird for you? Size, texture, flavor? If they are to be raised with your flock, behaviors might factor in. Are you planning on eating them yourself or selling the meat?
Should I feed them a meat bird feed?
Some people do. Up to a certain point the higher protein will help them grow faster and produce larger carcasses if that is your goal. If you do that you will be buying all that they eat. Some people like to reduce feed costs by pasturing them but those grow slower and don't get as big.
What age would be best for butchering?
Once the hormones of puberty hit the meat gains both texture and flavor. Some people like that flavor, some don't. There are some preferences on texture also but a big part of that is that texture determines how you have to cook it to assure it is "tender". A relatively young cockerel can be grilled or fried. Older and they can be roasted. Still older and you need to use a method that cooks them slowly and moist. The exception to that is to use a pressure cooker. With a pressure cooker the meat falls off of the bone but is cooked hot and fast. So how you cook it is one criteria.
Different cockerels mature at different rates so it is hard for me to give one age that covers every cockerel on the planet. Typically with my flock around 15 weeks of age is when those hormones are kicking in but some start a few weeks earlier or later.
Some cockerels grow faster and larger than others also, even from the same parent flock. I use this mainly to help me determine which cockerels I want to keep for my breeding flock. You can get quite a lot of difference in size even at the same age.
Some people start butchering cockerels around 12 weeks of age to try to stop them from mating the pullets or hens and stop them from crowing. There is not much meat there but it is very tender.
I find that around 16 weeks of age mine have finally put on a decent amount of meat. They have gained some texture and flavor but not much. Around 23 weeks mine have reached the end of their youth growth spurt and really slow down in weight gain. Some late bloomers can still be relatively small but it's where I set my upper limit.
I have no idea what is "best" for you. After trial and error I settled on what works for me. Good luck!