I think you are running out of room, not just for a rooster, but I think I would be reducing my flock. I have a very similar size set up, and through trial and error, I can run 10-12 full grown birds through the winter. I do run a rooster in my flock. More than that number of birds and there is a tension in the flock, they are just too crowded. Over crowding leads to lots of problems. My set up has multiple roosts inside and out, shade, in the winter a sun room.
Now in the summer time, I add chicks and get quite a bit above that number. However, the days are long and the nights are short. I free range most days for most of the day. But as winter comes on, the nights get long and the days get short, so they are spending HOURS more in the coop on the roost each day. By mid September, I start reducing my flock, and I need to be way close to that number 10-12 by the end of October.
If you have pullets, they are going to be getting bigger, I think you need to seriously reduce your numbers.
