Both my birds were rehomed/rescued, in fact my 13 year old CAG was owned by an old couple and she was cage bound for at least 4 years, she was only fed sunflower seeds, and occasionally got some fruit. So I'm seeing similarities here. However I worked VERY hard to get where I'm at with my Grey, she will now step up on command, and always give kisses when asked. But I also gave her, and still do, her space. My other Grey is more like velcro always wanting to be around me.
If you're wanting them to come hang out get a tree gym or something where they can be near you, but still have "their" space. I'm not sure if you're just trying to put them on your couch next to you, or on the floor, but get a neutral space for them that they can have. I bought a huge manzanita tree for Red, and everytime I was in the kitchen/living room since they're connected I would have her on her tree. I'd make no attempt to touch her other than to get her from point A to point B. I also noticed that it made her a LOT less jumpy to other noises in the house.
Now you have my 3 cents, I would get a neutral zone with something for her, in the event that you already don't. Treats go a long way, so don't forget that!