Hi, while they are in their cage(s) so much you have a brilliant opportunity to start bonding with them. What have you been doing to tame them? I would strongly suggest you look into target training if you haven't already. In the cage first is great and then when they're out.
I have had an Amazon and have a Mynah and an Alexandrine at the moment. I couldn't go near the Amazon, but her belly took her back to her cage! The Mynah will happily land on my hands and eat from them, but she won't "step-up" or do anything on command - she's my wild little thing and if I'm honest I haven't ever wanted anything different from her - so I save live mealworms for bribes/treats to get her in her cage. I drop them in her food bowl and then we play a game of how-quick-can-I-get-a-mealworm-and-can-Mum-shut-the-cage-in-time! Sometimes I have to shut the cage, give her another 10-15 minutes then wiggle to food bowl in front of her to remind her they're there and try again. I don't allow her free access to her cage when she is out and she doesn't get food while she is out so she will be hungry.
I can handle my Alex, but when he doesn't want to go in he won't! I have spent a few nights with him out, but the room is always secure before he comes out so I worry, but he's not at risk. If he's out all night I leave the cage open, but there's no food in there because I feed him in the morning and he's always finished by the evening. I'll feed him in the morning as usual and he usually goes in pretty quickly. I find he's worse if I haven't given him the out of cage time he needs the previous day. He's also target trained, which works brilliantly. He will follow the target into the cage 9/10 times - apart from when he's stubborn.
I've never kept my birds in their cages all the time, even when they weren't at all tame. I've generally relied on patience and access to food to get them back in.
Good luck. Let us know how you get on?
