Help - baby blackbird

Hi - last Thursday I found 3 baby blackbirds in the hedge who were being attacked by a cat. I managed to save one of them but wasn't sure what to do with it as there are cats EVERYWHERE in this neighbourhood - at least 11 different ones that I have counted who each pass through the garden several times a day.  The bird was very shaky and one of its wings was bent and one leg looked broken. It didn't appear to have any tail feathers but I don't know if that was due to the cat or if they don't grow them yet?

Anyway I decided to place it in our enclosed trampoline which has a net around it to keep the cats out and the parents are still flying in to feed it worms and berries multiple times a day. I wasn't sure if he would make it at first but 4 days on his wing and leg seem to have healed and he is now hopping around, cheaping and fluttering his wings to take him 3 or 4 cm off the ground a couple of times a day. He can't get very high but its got to be a start right?

I have been putting him in a transparent box with a lid with air holes but leaving him on the trampoline overnight as it is very icy here at the moment and heavy snow falls overnight. I have been leaving him and his box on the trampoline so his parents can see he is still there and safe and they don't fly off thinking he has gone.

Am I doing the right thing and when should I be releasing him? How should I do it? He is so much better than he was now but he can't really fly yet. Because there are so very many cats I fear I've saved him for 4 days and don't want to release him back to the cats. Should I be looking to find a bush to try to release him in? Should it be high or low? How do I do it so the parents can see where he is? What can I do to ensure he has the best chance of survival?

Thank you