Amanita - you will really not need 6 roosters for 20 birds. If you want to keep them that long, it is entirely up to you. A lot does depend on your location, your set up and your own personal goals. I commend you separating off your rooster chicks, they will terrorize the pullets if you don't.
It would be best to keep your pullets without any roosters until they begin to lay. At that time, I would want an older, proven rooster to be a flock master, and keep him with the girls all the time. I am not sure, but I would not recommend adding and pulling roosters multiple times a year. Chickens hate change. Anytime you add or remove a bird, there is a major power struggle and shift. It can be done, but will add a lot of tension to the flock for what purpose? This is the way I do it, and there are lots of ways to do it, just a suggestion.
If you have multiple breeds in your set up, and what to keep them pure, then you will need more roosters. However, a good active rooster should be able to cover all 14 pullets that you have. Personally, I do not like roosters that are raised with flock mates, I much prefer a rooster that is raised up in a multi- generational flock. Another idea, that you might consider is to keep those boys in a smaller area, and feed them well and harvest all of them in a couple of weeks. Roosters are cheap and easy to come by, a rooster raised in the flock, that is so nice, that they have not got quite to culling him. That is the rooster that you want. Then you would not have to wait so long to start hatching chicks.
Mrs K