I went back and read this posting again as I really wasn't satisfied with my reply, nothing unusual about this. I started a reply and had to stop to feed my birds, so I tried to post what I had. It didn't work.
Given the age of your Regent Parrot and the fact that he is fairly new to his new home, you have had to deal with the normal fear of new places and his loss of all that he was familiar with before coming to live with you, but you are having to deal with the fact that he is approaching if not already beginning to go through puberty. This is the time that he goes through many changes both in his body and in his personality, it is when he quits thinking like a child and begins to think like an adult bird and releases the parent/ child dependency type of bond for the more permanent mate bonding of an adult bird. It is a period when our efforts at training seems to be ineffective and is a good time to scale back on the training until he is done with puberty.
You have been pushing him a little bit too fast which is partly due to the puberty thing which has no doubt slowed his ability to adjust to his new home, so ease up on the training and concentrate on earning his trust just as you would with a new baby bird. This requires, as you said that you pretty much start all over again and spent this time learning more about his body language as well as increasing the variety of the fruits and vegetables that he will eat. It also requires you to spend time just hanging out with him just talking to him, read to him offer the occasional treat while talking to him. Don't reach into his cage to get him out or for anything other than to clean the cage and to provide him with food and water. I would open the door to his cage and take a step or two back away from his cage and let him come out on his own and service the cage at that time, after he comes out. Try to remember that this is a confusing time for him as well. He still has the drive to want to be with you ( the parent/ child bonding) and the drive to be more independent as he goes through puberty. It takes above average patience with him due to this particular timing, most of the time we only have to deal with one of these issues at a time but you are having to work through two major changes in his life, both of which are very confusing and stressful for a parrot.
Yes, he is an aviary type bird, which means that he is more suited for life in an aviary, but he can still be an excellent companion bird, but it will probably require you to spend more time and energy with interacting with him on a one on one basis.
I asked about his diet as free feeding pellets is really not much better than free feeding seeds. I think that he and your cockatiels would do better with eating partly cooked and/ or sprouted whole grains and a wider variety of vegetables along with some fruit for their breakfast and for all day long and just feeding the pellets for their dinner. The free feeding of pellets will interfere with how well he will respond to treats used either as bribery or for training purposes. This id due to the fact that the pellets and the highest value treats have one thing in common and that is the amount of protein in them. Also diets that are too high in protein extend their hormonal periods as well as increasing their aggressiveness in general.
As for understanding their body language better this link should help, as their body languages are all very similar regardless of the species of parrot.
http://littlefeatheredbuddies.com/info/ ... guage.html I am thinking that overall you have a fairly good grasp of what to do provided that you are patient and allow the bird to come to you as well as letting it set the pace for interactions and training. If the bird moves away or simply refuses that is fine, do something else for a short while and try again in a few minutes.