I like your ideas! But a question about his sleeping box; do you believe it resembles a nest box from his POV? If so, replacing it with a cage may improve behavior. Nest boxes (or similar) can stoke breeding and territorial instincts, even at a young age. Generally, the largest cage reasonably appropriate for the bird and your home is preferable. Stock it with lots of diverse toys and you will soon learn which ones are enjoyed. Hopefully the cage will be viewed as a place to sleep, rest, eat, and play. Some prefer cages with play-tops while others enjoy the dome-tops that give an extra dimension.
Exactly what I thought as soon as you wrote the word "box"! He/she is approaching the age of possible sexual maturity, all birds are different as to when that starts, some early, some late. I know you don't know his/her sex, I think spending $20-$30 to get him DNA sexed would be useful, not only for helping with behavioral issues, but also health issues he/she might experience in the future. I always get all of my birds DNA sexed because as a breeder of 20+ years I want to know if each particular bird may become egg-bound. That way if they start displaying any symptoms of illness or pain I can rule out egg-binding immediately, or I can start taking action to help them out. It's cheap and it's well worth the money. You can have it done at your avian vet or you can Google search "DNA Sexing For Birds" and there will be several labs online that you can order the kit from, they'll mail it to you, you either pluck a couple small feathers from your bird's chest or some of the kits have you clip a toenail very slightly, put a tiny drop of blood on a cotton swab or on a paper card, and then you send it in. You'll have results in a couple of weeks.
As far as his/her current behavior, yes, you're correct that this is most likely a mix of territoriality and possibly a hormonal issue as well. If your bird has started to go through hormonal periods and you provide a "box" of any kind for him, especially if that's where he sleeps every night, this can enhance nesting behavior. It can also actually bring on the hormonal behavior for the first time, earlier than when he/she would have started it naturally. This is why breeders use "nest boxes" and attach them to their bird's cages. Just hanging up a nest box in the cage of a bonded pair of birds that are not interested in mating at that particular time can kick them into breeding mode and get them mating. So I'd ditch the box.
Yes, your bird should have his own cage. First, he needs a space to call his own, full of toys, food, treats, a swing, etc. that are all his, and that he can go and entertain himself with, and that will keep him from getting bored. You don't necessarily have to lock him inside it at all (unless there is no one home) but he needs to be able to go inside his space whenever he wants to. Second, a cage provides your bird with his own space that makes him feel "safe". There is a big difference between a bird having a cage with 4 "walls" and a bird having a place set up for it out in the open. Yes it's his space, but he's not protected at all in his space right now. Inside their cage most birds feel very comfortable, safe, and secure. This is why even birds that are not at all tame, that act wildly when they are out in the open, act calmly when they are inside their cages.
Now placement of your bird's cage is very important, as you do not want to put it in a place where he will be away from you and the other people in your house, and where he isn't part of the action and right in the middle of it. Your bird's new cage should be set up in the main living room, TV room, den, etc., the room of your house where you and you family spend most of your time together, where you are after work and on weekends, where you guys hang out in the evenings, etc. Like I said, you don't have to lock him inside his cage at all, my birds all have their own cages located in my living room, and the only time I put them in their cages and shut the doors is when I'm not home. So in the morning before work, after work, on days off, and on weekends all of my birds have their cages wide open. I am usually in that living room watching TV, reading, playing guitar, playing video games, whatever it is I'm doing, and my birds might be in their cages playing with their toys, eating, or napping, they might be on top of their cages playing with the toys up there, eating from their bowls up there, or just sitting up there napping, they might be on the huge PVC play gym that is also in the same room playing, or they might be on my shoulders hanging with me. No matter what they're doing or where they are in the room, the important things are that #1 they are in my presence and the presence of anyone else that's in my house and they aren't missing anything going on (important to constant socialization), and #2 they are able to go back to their own cages at any time they may want to, giving them a huge sense of security. Just knowing that they have their very own space that is safe and they can go to it any time they want to is a big deal.
Now my birds have their own separate, small sleeping cages in my master bedroom (my 4 larger birds; my 7 budgies are in a large flight cage in my living room and they get covered at sunset and sleep there). I feed my birds dinner (they eat with me) in their large, main cages in my living room about a half an hour before the sunset starts. After they are done eating I say"OK, night night, sleep sleep time!" and they follow me upstairs to my bedroom. They each get in their much smaller sleeping cages (these have no toys, just a swing and a dish of water) and I kiss them each goodnight and cover them. Then I go back downstairs to the living room and say goodnight to my budgies and cover their cage. I'm usually awake until around 11:00 p.m. or so, depending on the day, and I just go upstairs to my bedroom and go to bed. They never wake up or make any noise when I walk into my bedroom, like I said earlier, when they're covered up they're dead to the world. Then in the morning they are always up at sunrise because they can see the light through their covers. On work days I'm up earlier than them anyway and I don't remove their cage covers until the sunrise starts. On days that I do not have to get up before sunrise they are generally awake at sunrise because they can see it through the cage cover, but usually they let me sleep for maybe an hour past sunrise, maybe, lol. 7:00 a.m. is late for me to get up (the 7 budgies in the flight cage downstairs in the living room are up at dawn and are LOUD). You can do this however you want to do it, but don't think that you cannot have your bird's new cage in your main living room because he/she won't be able to sleep at night while you are talking, watching TV, making noise and moving around in the same room. It's not true at all. All you need to do is throw a cover over your bird's cage when it's his bedtime. Trust me, the noise, lights, light from the TV, talking, etc. will not keep him awake at all. It's amazing how they are completely out as soon as that cover is put over their cage.
A part of controlling/ending your bird's hormonal behavior is getting him on a strict sleeping schedule that corresponds with the natural sunrise and the sunset every day, and if you strictly follow this "Solar Schedule" (search this in the forum search bar and you'll get numerous explanations and examples of aggressive behavior and biting being stopped by putting a bird on this schedule) and your bird starts getting at least 12 hours of sleep every night, your bird should be knocked out of any type of hormonal or "breeding mode"/"breeding season" in 2-3 weeks or so. Following this new "Solar Schedule" and allowing your bird to get at least 12 hours of sleep per night combined with getting him his own, big cage filled with his own toys, treats, etc. located in the main traffic/living area of your house should help tremendously, and should stop his territorial and hormonal behaviors. But you have to follow the Solar Schedule strictly and ensure he's getting enough sleep, this is key.
"Dance like nobody's watching..."