You are so sure of what you think you know... Bless you for that but, if you want to become a good bird keeper, there is one lesson you need to learn. A lesson that people who has had many, many birds under their care have learned the hard way: people are not good at figuring out what birds want or like. We can't read them accurately. We think we do but we don't because we base our observations of their behavior in what we do know: mammals. And birds are completely different from them. You can keep a single dog or you can keep a pack of dogs and both the dog living single and the dogs living with other dogs can be happy - but dogs, regardless of breed, are one single species that has been domesticated for over 30,000 years. Parrots are all different species and they are all undomesticated so their needs are identical to the needs of the wild ones. Some of them are only happy when they have others of their own species and some of them can be happy with just one person as long as this person has his/her entire life revolving around the parrot (which not that many people are willing or able to do). The truth is that there isn't a whole lot of leeway in what makes them happy because we cannot change genetic traits.
You can't keep a lone tiel, a lone budgie and a lone GCC and expect all three of them to be happy. It won't work. It might (and this is a BIG might and I am only saying this not because I actually believe it will happen but because everything is possible) work while they are still young but it won't work in the long term. I can assure you (and you can take that to the bank!) that both your tiel and your budgie will like a mate if they are sexually developed, that is! It's just a matter of getting a bird of the appropriate gender and age and introducing them the right way.
I know that you think you know your tiel and that he doesn't like other tiels but you are basing your entire premise on the occasional perceived behavior of a baby in a very stressful situation (a few visits to a petstore). I am basing mine on nature's decrees, other experienced people's experience and my own personal experience of more than 50 individuals of either species. I have never seen or heard of a tiel or a budgie that did not like another of their own species if the other bird was right and the transition done correctly. Not once. The ONLY tiel I've had which did not like all other tiels was an old blind female with liver damage that had no toes left in her feet so she couldn't see, climb, perch or fly - and I still managed to get her a mate she accepted and liked! It took time and a very gradual approach but it worked and she lived the last couple of years of her life happily cuddling with her mate.
We have a huge obligation to any animal we take in as our own and it's not only food and water. It's our duty to make sure they are as happy as they can be at any point in their lives. Birds change as they mature - they get needs they did not have before and, whereas before they were OK with certain things, as time goes by, they are no longer OK with them. How long have you had your birds and how old are they?