Hi, Em and ekkie, welcome to the forum [you did not tell us what his name is].
Now, just a clarification: your parrot was hand-reared because he was hand-fed so, although he was not handled frequently by it's own human [which is terribly unfortunate for him because it traumatized him for life], he is imprinted to humans and do not need 'taming'. It might take you longer to win him over but, as a bird that was not SEVERELY neglected or abused, he is perfectly 'redeemable'... it's just a matter of doing the right thing and waiting patiently for him to make up his mind that you are worthy of his love.
Now, as to what is the right thing, well, for one thing, you should not be putting your hand inside his cage. This is a no-no with all parrots that were bought or adopted when already a juvenile, young adult or full adult. It can only be done with babies and then only babies that have been well treated by the breeder. You need to earn the trust that will allow you to go into his cage when he is in it - you haven't yet and that's why he tries to bite you when you do. I would strongly urge you to stop doing this because you are not helping your cause by it - quite the contrary, you are teaching him that you will do whatever you want regardless of what he wishes or doesn't wish and that, in a nutshell, is the reason why pet parrots learn to bite humans. You see, parrots are not naturally aggressive. They don't have the gene for it because they are not predators so they don't need violence to survive [kill a prey so they can eat] or belong to a hierarchical society where lower individuals need to fight their way to the top [for better food and procreation]. Parrots only bite [or attempt to] to defend or protect themselves, their mates, their babies and their nest. But they are very smart, they study situations, reach conclusions and learn from past experiences so you do NOT want your parrot to reach the conclusion that you will not listen to his wishes and learn that the only way for him to get you to listen is for him to bite you. It's the old 'slippery slope' and you do not want to go that way.
All my parrots came as adults and from somewhere else, some of them with biting issues and these issues have all been resolved with patience, respect, consistency and persistence. Your parrot is very young and still malleable so if you do the right thing, he will be a loving companion to you for many years to come [well, not as many as with other species because all ekkies die young due to their specialized diet but a good 15 years for sure].
Put his cage high enought that his roosting perch is at your eye level when you are standing up, make sure that the back is solid [either by being placed against a wall or by draping a thick material over the back of it], don't stare at him [only predators do that], spend as much time as you can in the same room his cage is, talk, sing, whistle and, every now and then, offer him a treat without asking or expecting anything in return. And don't put your hand in his cage when he is in it -clean it when he is out of it and offer the treats from the outside of the cage and, if he doesn't take them, just leave them there for him to take and walk away.
Now, you did not ask about these things but I feel compelled to mention them because ekkies are the most difficult species to keep healthy and happy in captivity and these are diet and light schedule. Ekkies require a super specialized diet: very low protein, very low fat, very high moisture and super duper high fiber of the right kind - this means they cannot be free-fed any protein food which is true of any parrot but, with ekkies, it also means that you cannot feed it pellets at all. Some of them are also intolerant of salycilate so you will need to make sure he doesn't get produce that is high on it [and this is super difficult because virtually all fruits you get in the supermarket are high in it as they are picked green!]. And, because they have the longest breeding season of all parrots, you will need to be super vigilant of its solar light schedule or he will end up overly-hormonal all year round.
Ekkies are outstandingly beautiful birds [I had a redsided male -Romeo- and a Solomon female -Elsa, poor Romeo was a MEAN [he was the very first parrot I heard growling to people] plucking/barbering mess and Elsa only loved men and hated all women] but, in truth, it was a huge disservice we did them when we bred them for the pet trade because they are waaaay too difficult to keep healthy and happy in captivity [rescuers use to refer to Laurella Desborough, one of the first ekkies breeders here in USA, as Cruella Desborough
] so, please, do a lot of in-depth research about them and their proper diet - and I don't mean go to a breeders or a 'fluff' birdsite where people who never did any scientific research give their own opinions, I mean REAL research like studies, field biologists reports and.or blogs, etc.