Yes, that would work.
However, if you have 4 hen coops, then only keep 4 breeds. Then eliminate the extra roosters. If you want to breed chicks to sell, you have to get a bit heartless, and a lot of them should not make the cut. If you hatch out chicks, a lot of them will be male, and you really can't keep all of them.
"How do I implement this and make sure my roosters are as content as they can be?" This worries me, if you cannot cull birds, you really should not breed birds. People would like to think that a bachelor pad will let them keep all of their roosters in perfect harmony, and that is seeing chickens in a non realistic way. The truth is the bachelor pad idea often work only for a limited time, will not work at all for some roosters.
If you have the fifth coop - if your coops are different sizes, make the fifth coop the biggest one, and that is where you will keep your layers, with no rooster. These are just for eating eggs.
In the smaller coops you put the breeds rooster, and then using the SOP (Standards of Perfection) for each breed, evaluate each hen. If you have multiple roosters of each breed, pick the best one based on the SOP too. Pick your top hens, and rooster and keep them together in the smaller pen. The other birds of this breed that are farther from the SOP should just be in the laying flock.
Then you should also get something to weigh birds. You should have a number system identification for each bird. And you should record eggs collected each day from each coop, weights and growth of chicks, date of first laying. With the idea of over say a decade of careful breeding, you actually produce hens with good feed to growth conversion, good laying, and match the SOP.
As you hatch and sell, you will need a way to deal with the excess males. You do have a window of about +/- 12 weeks. After that you need a grow out pen, and plan of processing them by 16 weeks.
Now, those are plans you should strive for, but you don't need to do them by Tuesday. I would break this down, into a 5 year plan. I would advise just starting with two breeds. The best two breeds that you have based on the SOP's.
Note that once you separate birds, it is pretty difficult to get them back together. I would plan to keep them separate 100% of the time. I agree with AArt in that you do not need to worry about inbreeding for the first couple of years, then just add new and better roosters, and keep your best pullets.
This can be a life long hobby. In today's world, you can reach out to professional breeders (most who started just like you). get better birds, higher quality roosters generally are the best way of improving your breeds and are reasonably priced, and may even be free. Look around locally for 4-H groups, or poultry clubs. It is fun to show birds, and be with other people that love chickens.
Mrs K
