My birds stay quiet for 8-9 hours, sometimes more. If I put them to bed late, they will wake up late with me. But they are smaller birds than cockatoos (maroon belly conure and caique). I also make a point of getting them out to have breakfast in the kitchen with me. I think this really helps them feel that we are doing things as a flock. My rescue nanday doesnt have a night cage yet, but she stays quiet until she hears me up and about.
Getting your birds adjusted might be a challenge. My two are 12 and 13 yoa and have been in night cages since they were very young, but it sounds like your birds are young also.
I think I started by having their night cages next to the bed with food, water and toys. I would put them in the cage at night where they could see me and feel safe. I would read or surf the internet in bed with the light on, so they felt comfortable with the cage and that we were together. After I turned the light off, I would cover the caique's cage. Eventually, I moved it to a quieter darker area but where he still felt close to me. He is very in tune to me and if I leave the bedroom after he is in his night cage, he will call for me. Rarely, he will call me in the middle of the night and wake me up, I think because he hears a noise or has a bad dream. I tell him everything is okay and he goes back to sleep. I dont mind if he wakes me up because he is scared. I have made the mistake of getting him out and snuggling him. Getting him back into the night cage is a challenge then. He is no fool. The next few nights, he will repeat the mournful cries, hoping I will take him out and snuggle him again. They can be manipulative creatures, so watch out.
I have a cheap travel cage for the caique, but I dont know where to buy it. For the conure, I have this cage, but in the 24" smaller version:
Petco Designer White Finch Flight Cage - Finch Flight Bird Cage from petco.com
I also have some of these cages in this size for travel cages in case I ever need one.
This is another great cage, but expensive.
King's Cages - Avian and Pet Bird Cages, Supplies, Food, Toys, Perches, Aviaries, Pluck No More
Be sure to provide water in their night cages. I clean the water dishes every night before I put them to bed. I would give them some dry food and maybe a treat to start off with.