It sounds like you are in an enviable position with those ages. They are integrated, peacefully coexisting. Life is good!
I don't know how big that little coop is but if all they use it for is predator or weather protection when they are sleeping they are fine. They are not being hurt in any way by sleeping on the coop floor. I don't see a huge rush to force them to move. What kind of roost space does that little one have? Mine normally transition to the roosts about 10 to 12 weeks so yours are not off schedule as far as roosting that much, differences in the configuration may affect when they move to roosts too. Normally I have more than twice as many as you do sleeping in a group on the floor and I have yet to have one suffocate. This is in my grow-out coop with no adults present.
How big, in feet or meters, is that big coop? How well will it fit 15 grown chickens? Is it big enough for you to make some modifications inside if you need to? What do your current roosts look like in the big coop? How much linear space and how are they laid out? How high are they? Are they higher than the nests and high enough the adults cannot peck the feet of those on the roosts? If hey are high enough that makes them a safe haven of sorts.
My brooder-raised immature chickens never sleep on the roosts with the adults until they mature enough to force their way into the pecking order. That's normally about when they start to lay. It is pretty normal for mature hens to peck at juveniles if the juveniles get close at all on the roosts. If your roosts are big enough and spread out enough where the adults all sleep on one end and the juveniles can crowd into a far corner it might work, but it's usually my brooder raised juveniles that try that, not the brooder-raised. Even then I've seen a hen leave her normal roosting spot and go to the far end of the roosts to beat up the juveniles.
Until they mature enough, mine look for a safer place to sleep. That might be a place in a group on the floor. It might be on some stuff I have jut off the coop floor. It could be the nests. (I think this is where a lot of the problems with chickens sleeping in nests come from). I integrate younger chickens all the time. The problems with them sleeping in nests became so regular that I installed a juvenile roost higher than the nests but lower than the main roosts and horizontally separated to give them a safe place to go that is not my nests. That's worked out really well, but I still have some groups that sleep on the coop floor until they mature enough to transition to the main roosts. If I find a chick sleeping in the nests (maybe once every three years) I put it on the juvenile roost after dark. One time usually takes care of that.
I'm going through all this so you are prepared when yours go inside. Don't expect them to share the main roosts with the adults. It might happen but it is extremely unlikely in my experience. If yours start sleeping in the nests you may have a solution with a juvenile roost. It is also quite possible you will not have any sleeping in the nests.
If yours have been ranging together during the day without issues and your coop is big enough, you probably won't have big issues when they move to the big coop. The first morning or two after that I'm down there pretty early to open the pop door in case there are issues, but there never have been in my big coop. Usually I find the juveniles on the roosts while the adults are on the floor once they have been awake a bit. That's the young avoiding the older. Perfectly normal.
Some or all of yours might move into the adult coop on their own. It occasionally happens. But usually I move them in. After they have gone to roost I move them from the grow-out coop to the main coop and lock them in there, just putting them on the main coop floor. I lock up the smaller coop. The next night they may all sleep in the main coop on their own. Sometimes I have to move them inside for a few nights until they get the message. Leaving the old coop locked and unavailable helps with the transition.
Good luck!