First, I want to say you seem to have great instincts with the bird. Your progress is good. Trust what you think will work and try it.
My daughter's bourkes, Stanley, seems very people oriented to me. I consider him quite well bonded to her.
He eats out of our hands. He will follow an oat groat or piece of oatmeal around to do a kind of "trick". He will turn in a circle, walk from across a table and onto a hand, etc. for an oat. We don't work with him on this much. I think he would be quite amenable to more of this if we spent more time on it. He sits on our shoulders for lengthy periods of time, plays in our hair, goes potty on the "potty stand", and allows gentle petting in the direction of his feathers only. He says "pretty" and "step up", but not very clearly and in a little bird voice. He will chirp to us or say his words in order to get us to come to see him in his cage. He will come out of the cage to see us and step up from any place inside the cage when we put our hands in and ask. He will go to any stranger, adult or child, if we tell him to step up for them.
He will do things for my daughter he won't do for anyone else. She can get him to lie on his back in her hands. She rubs him against her face and kisses him on the head and on the outside of the beak.
I attribute most of his friendliness with people to the fact that we bought him when he was almost, but not completely feathered out, and visited him at the bird store often until he was weaned. My daughter would watch the other customers playing and bonding with their birds, and she didn't have any idea that a bourkes shouldn't react the way the bigger, "friendlier" birds reacted to socialization. I'd read articles that said he wouldn't do so many things, and I'd try to tell her he wouldn't like something when she would try it, but before I could get the sentence finished she'd have him accepting it, so I finally decided to just leave her alone and let her try whatever she wanted. (Of course, it had to be safe.)
The only advice I would offer you regarding continuing your bonding process with Twitter is to not be afraid to try anything you have been comfortable doing with any of your other birds.
Bourkes are thinkers. They do almost freeze and study the environment when they are uncomfortable. Don't let that lead you to believe they don't like to play and cut up once they feel safe to try it. Of course, if you notice your bird having a fear reaction that causes a retreat, back off, but for the most part, Stanley will get used to stuff fairly easily. I've actually never seen him run away from anything.
Stanley was an only bird for several months. During that time he developed quite a little personality, but his personality blossomed after our senegal joined our home. She is too big to allow them to interact, but their cages are close. He watches her and he copies her. He always played with his toys, although it used to take him a few days after a new toy entered his cage before he would explore it, but after he watched her he picked up new ways to play. He loves swinging toys, and he mostly just sits on top of them and swings them, but I even saw him try hanging from the bottom of one once, as if he were trying to play like she does. He only did it once, and perhaps he will not repeat it because perhaps it was just too much for him, but I am certain he tried it because he saw her have so much fun doing it.
He is jealous, so they both compete for our attention. I am trying, unsuccessfully I might add, to teach the senegal to limit her contact SCREECH. I will lavish all sorts of attention on Stanley when he makes his beautiful chirps. (And don't you just love every chirp a bourkes makes?) It works when I am in the room. The senegal imitates him perfectly when I am in the room. They have contests to see who can say "pretty" with the sweetest voice. Stanley absolutely WILL copy things the other birds do to get good attention.
Having said that, I want to mention that I have read repeatedly that budgies are too aggressive to house with bourkes. This doesn't mean I would say do not get a budgie if you want one. A senegal is CERTAINLY too large a bird to house with a bourkes. I simply don't let the two come into direct contact with one another. Stanley loves having Roni around, and she loves having him around. You might even be able to allow a budgie and a bourkes supervised play time together. I just do not know. I only know all the literature states budgies are too aggressive to house with bourkes, and even at the bird store from whence Stanley came, they would not put budgies, even baby budgies, in a cage with the bourkes because the budgies would bully them.
Years ago I had some birds, but I had been birdless until Stanley for about thirteen years. I had severe allergies - I thought to the birds. It turned out I am actually allergic to gluten. One of the birds we had was a lory. Dry lory food gets air bourne, so it was probably the wheat in that which made me so sick. However, I did rehome all of my birds at that time, thinking I was allergic to them.
I learned I was allergic to gluten, and after I stopped eating it, when my daughter kept begging me for a bird, we got Stanley. We spent a lot of time in the bird store first to try to be certain I wouldn't have an allergic reaction. So far so good, BUT, as much as I love cockatiels, I will never try a cockatiel again. I just won't take a chance with that dander. I also will never try another lory because of the powdery, gluten filled diet. I mention that because I think cockatiels are the sweetest birds ever. Go ahead and try to treat your bourkes as much like a cockatiel as you want to. I doubt it will hinder your relationship with him, but I also doubt he will ever respond like a cockatiel. Really, does any bird compare to a cockatiel?
I have no idea how safe a cockatiel would be around a bourkes, but, again, the worst that could happen if you get another cockatiel would be that you could let the birds interact from afar as do my bourkes and my senegal.
We did recently add both the splendid and our soon to come home linnie to our family. Those three birds do fairly well playing together. Stanley is learning to share his things with the splendid, and to tell you the truth, if he doesn't become happier about it within a very short time, I'm going to give into his pouting and get another cage so he doesn't have to share. Right now I'm trying to get either Stanley and the splendid to enjoy sharing a huge cage or, if that won't work, the splendid and the linnie, since they have neither one ever lived singly in a cage. If none of them want to share - well, its only money for another cage - and space lost - and time - all unimportant issues in comparison to their happiness and feelings of safety.
So I guess to sum up, I'm happy to hear from someone else who is owned by a bourkes. Don't let what you read about bourkes limit your hope for what you can eventually build in a relationship with Twitter. Keep in mind the bourkes personality trait to freeze when under stress and study, study, study the environment, but go ahead and introduce him to whatever you want him to do. If you want another bird just because YOU want another bird, go for it. It will enrich Twitter's world even if they can't actually play together. However, don't get another bird unless you want the second bird for itself. Twitter can become a wonderful companion as a sole bird.
One other thing I forgot earlier. Stanley was purchased before he completely feathered out, but all of his clutchmates were purchased much older, older than you purchased Twitter. They all became trusting companions just like Stanley when handled daily. (Well, maybe no one is JUST like Stanley.) Additionally, my 21 year old son, who also has no preconcieved notions about how the grasskeets should behave, can get both the bourkes and the splendid to hang upside down from his fingers. I don't see that as being part of the "nature" of a grasskeet, but, again, ignorance seems to be bliss. None of them read the books.
Your pictures of Twitter are beautiful. For the holidays I'm going to try to persuade my sons to teach me to post pictures. With this economy, neither has much money to spend on ole mom, so I should be able to get a bit of time out of them.