OP I have read through your posts and hope I can offer advise to help you train your birds.
1. The mix of king pigeon and homer will seriously hamper the birds performance. The mix breed birds will be too heavy to fly as well as the pure homers. They likely will also have the temperament of the kings and lack the desire to fly high in the air, or to even fly for any length of time. This is not just a physical ability thing, it seems to be in their nature not to enjoy flying, like many other fancy or show breeds.
I suggest you stop breeding from the larger birds, and only breed form the smaller, better flying ones. You can use the bigger birds to foster eggs and squabs from you best birds to increase the number of good flyers quickly.
Then you could eat the big birds (pigeon pie is delicious), or keep them as pets if you are attacked to them.
2. Keep breeding birds in their own section, flying birds in another. Use the none breeding birds to train to fly.
3. The non breeding birds need to go on reduced feed to get fit and make them hungry so are more easy to train. If they are over weight they won't be able to physically fly for long periods, and if they are not hungry they will have little desire to return to the coop when called.
I suggest feeding them once a day in the late afternoon when you call them in from flying.
4. Let the flying birds out at the same time each day. Now they are used to their home, you can safely gently chase them out of the coop. If they are reluctant to fly use a flag or something to wave about and scare them into the air.
It will take a few weeks of a good diet, flying to build muscles and fitness, but eventually they should naturally all come out of the coop and take to the air and stay flying longer and longer before they land.
Call them in when its feeding time, and as they are hungry they should all come in very quickly at once. If they hang back, or a few don't come in you know you are overfeeding them.
Always have water, grit, minerals etc available to them in the coop, but just the feed 1 time a day. Let them eat as much as they want and take away the feeder after the last birds loose interest.
Good luck.