Milage may vary-- I've had a bit of this with Luxie on my shoulder, who would bite my earlobes and the back of my neck. I've not done the back-to-the-cage response because of how much of a cage-body she can be, but if I recall one of the responses can be a calm but firm "no" and to the cage for a bit with you leaving the room briefly (another thing I can't yet do because of current living situation). I think it was StarlingWings that this worked for with budgie Mallorn? (Please correct me if I am wrong!)
What has worked for me thus far is calmly but clearly saying "ow," and pressing on Luxie's beak gently but firmly. I can miss sometimes, since the target is out of my vision, but the because it would unbalance her and gently startle her, it would interrupt the behavior. While it didn't look like any change happened immediately, over the course of several weeks, she has done it less and less, and has learned how to nibble so gently it doesn't hurt. I also give her praise when she does the gentle nibble. When she does bite harder, she kind of knows the annoying finger is coming and reacts defensively, but the consequence stands and she lightens up afterward. She bites maybe 1/5 shoulder sits now, as opposed to 4/5 after her new-home submissiveness wore off. Learning process an' all.
This is based off my observations that her preference for my shoulder when out was strong enough not to dislodge, and that a cage return would not work for her. She has occasionally flown on her own back to the cage when I poke when she's more in a mood, but does not seem to have dented the bond overall. No guarantees, but maybe something of use here.