As I mentioned above the far end of mine was sometimes below freezing, but the warmest spot was toasty. Not in summer, of course, but in winter. My brooder is obviously outside. 85° is not going to cook them or be too warm no matter how old they get but don't be afraid of having the cool spot really cool. They can handle it and, in my opinion, it's beneficial for them to have a range of temperatures. They generally feather out faster and acclimate better. I imagine your room temperature in that bathroom is in the 70's. I'd prefer a brooder big enough and ventilated enough so the far end could at least get that cool. There is a lot of personal reference in that, like I said 85 won't hurt them, but I think you aren't getting them ready for outside as much as you could be by coddling them. I don't see what the downside of the brooder taking up the whole shower is. To me that sounds like a plus but you are looking at it and cleaning it.
I don't like to split them up once they are integrated. You don't want to make that any harder than it has to be. Why create a problem that doesn't currently exist?
I don't know when your 12 chicks will outgrow that brooder. It's not a square foot per chick thing, each brood is different. They grow very fast. Overcrowding can lead to aggression and violence, that's the behaviors you want to look out for and avoid if you can. That can be feather-picking, pecking each other, or fighting. At some point there will be some fighting anyway, even if they are all girls, but that's just playing and practicing, usually nothing serious to worry about.
The bigger they get the more they poop. If that is in a small space you may wind up managing poop a lot. If they have more room it doesn't build up quite so fast.
I don't know what your situation is outside, temperatures or what your facilities look like. It sounds like you may already have older chickens out there. "running around scratching and pecking at the floor bedding like the older chicks do" Some people like to keep chicks inside. They may want to watch then grow up, especially fi they have kids. It is easier to tame them and turn them into lap chickens if you raise them inside. Lots of people prefer that.
My personal preference is to get them outside as soon as I can, which means when I take them out of the incubator or pick them up at the post office. That way I avoid any potential smell, noise, and dust which goes a long way to keep my wife from divorcing me. I believe it helps strengthen their immune system by exposing then to the environment they will be living in as early as I can and still closely monitor them in the brooder. I think raising them across wire from the flock makes integration easier. I don't know what your goals are or what you have to work with but moving them outside might be an easy way t get them more room.