Welcome!!!! For Melon (she's a IRN tho) she took me a good few months, and even still I have a lot to learn as she was a rescue from the wild! I hope I can help some but since every bird is different I can't promise it may or may not help!
The first month was letting Melon adjust to her new home as a pet (and as a new family ofcourse!), due to the fact she was never used to being cages, etc, I would sit next to her cage and talk to her when ever I could. But also to give her space as well.
The second month, I found out she likes oranges!! So I used orange as a form of treat for her and eventually she started to warm up to me and my s.o, she also stopped trying to dig at the corner of her cage (thank goodness.)
From then on she started to open up and started to get more and more comfortable with her new life. However she became cage bound in the process.... (Which I think is happening to your birds.) she gets very aggressive when I or my s.o would stick our hand in to have her step-up, she would lunge and had even gave me a significant amount of good sized bites! (Yikes)
I've had her for about almost a year and she's still kind of cage bound but we're working on that. Now she can step up, and she's much comfortable with me. Even then she still lunges at me with full intention to bite (only at night time and I don't know why yet... we're working on it!)
First thing's first, I would definitely keep up with sitting by the cage and talk to them! (Because they seem to be very afraid of human presence, from what you described.)
When they stop flying to the back of the cage when ever you are next to or near the cage, try to sit next to the cage and put your hand inside the cage, and talk to them. (Melon liked it when I soft softly to her) it's okay if they fly to the back of the cage as everything takes time and patience! (Well worth it once your birds open up to you)
You'll notice your birds will eventually get used to your hand, try hold a treat in your hand and see if they'll take to it. (Millets are definitely great! And ringnecks love fruit so perhaps you can try to experiment on which fresh fruit they like as well!!)
i hope this kinda helps you. This is how I learned to gain Melon's trust and am slowly bonding with her. Everything does take a lot of time and patience, but it's well worth the wait!!
Melon also says welcome!!
