Hi, Sam, and welcome to the forum! I have two LSC (actually, they are Eleanora mixes because they don't have the bright yellow cheeks), both of them came to me after belonging to other people. Freddy was 21 (he is now 25) and Linus was 25 (he is now 26). Freddy was a screamer and Linus a real bad plucker. Freddy is now OK but Linus will need a couple more years to stop plucking, if he ever does (he has gotten much better though).
As to getting a parrot to accept a number of people equally... well, although it's not completely unheard of, it is not the usual. As I am sure you know, cockatoos are monogamous and, as such, they choose one individual to become their human and, even though they could be friendly to other people, they will never develop the same relationship as they do with their chosen one. Now, when one gets a baby and this baby is always treated with love and patience, the adult bird might (not a sure thing) be willing to trust a number of people that are familiar to it BUT when you are talking about birds that come to us as adults and which might have been neglected (and, in captivity, neglecting a cockatoo is more the rule than the exception) or even abused, this small margin of exception kind of disappears and, if lucky and the new owner/human does everything right all the time, the bird will bond with one person and one person alone. So, the question here is: Is there one person he never bites? One person for whom he is always more than willing to come out of his enclosure? Because, if there is, I would suggest only this person handles him.
As to 'taking reinforcement during training', are you talking about the reward for doing something right? If you are, is he been free-fed protein food? Because, if he is, the answer is simple: not enough 'reward' in the reward
High value items need to be identified and used ONLY for training. Also, training needs to come after bonding or it doesn't work in the long run so, again, you need to identify his 'chosen one' and this person needs to be with him hours every day just bonding (cockatoos are SUPER needy and need long hours everyday of personal attention). If the training is done right (and this is a big IF, mind you!), it can deepen the bond but the bond needs to be there first and, with neglected birds, it becomes more of a need than with well-adjusted birds that have been raised from infancy because the lack has created psychological problems (lack of trust, disaffection, depression and even PTSD) that need to be addressed before any training is done. A neglected or abused bird is in a negative number position and it needs to be brought to a zero with impeccable husbandry (solar light schedule, fresh food diet, steady and strict daily routines, etc as well as plain old familiarity between the bird and the human), then you start adding positive numbers by creating the bond (hours and hours daily of company and love) and, later on, with training. You can't jump from -10 to +10 in one single leap (training), you need to go number to number and build up.