More help with Charlie please

I am having trouble with getting her back in the cage. She loves to sit on the top of the cage with it open...however when it comes time to get her back in the cage at night I have yet to find a way...I have tried different foods and treats but nothing works...if I try to "encourage her" I use a chop stick she is not afraid of it but I can gentle touch/push her over to the side and she will sometimes climb down.... but other times she just lets go and falls to the bottom of the cage being that she is missing a wing she can't catch herself...I don't want her to get hurt but I also want her to be able to have her out of cage time....If I just leave the cage door open it is even harder to get her back in and she will sometimes flop onto the floor...then I have to chase her around and towel her to get her in...I still can't touch her...I don't want to make it worse but she seems to like being on her cage instead of just in it...PS she hates sticks and hand held perches she will try and fly/get away and ends up doing a belly flop...so I am having trouble getting her to step up on anything
Here she is gently mouthing the chopsticks

Here she is hanging out on the cage

Sounds like you've already tried the basic things...maybe you can just reward her tons for going into the cage. Once you get her in (however you do it) give her tons of her favorite treat or whatever else she likes. Another thing that might help is if you put her in and then let her out again a few times so that she doesn't think that going in the cage means being stuck there. Good luck!

I had many late night's in the beginning with Bosley because he wouldn't go in.
I wouldnt try to force her in like you are now, will only become a habit and make it harder in the long run.A few things I did was not let Bosley on the top that way, makes it harder to reach him and I dont trust those tops. I have a T stand with wheels that is right outside his cage he can perch on. I alsoade sure that at night he got no treats till bedtime and when he was hungry he would get the nut I put in his cage. Also dimming lights can help.
The good news is after the trust was established I can pick him up from anywhere and he even goes in his cage at dark now and asks for his nighttime nut.

Don't feed the high protein food all day long, give it to her when the sun is beginning to go down (no artificial lights on) and put it inside her cage. She will go in by herself.

She gets her pellets in the am and her veggies at night