Glad to hear you have a sweetheart, but refuses to step up, she may have some kind of phobia relating to her two previous homes that she either doesn't trust hands or like Dan described, she doesn't think they are a stable perch. You will have to work on getting her to step up but it may take lots of time. She needs to trust you and with this being her third home she is going to be very hesitant to do so.
Just continue to do as you described but mix in some stepping up lessons and I think eventually she will do it. Just be patient, very patient, but at least she is allowing you to scoop her up and that is something that most will not allow, so be grateful for that.