If they won't go into the cage, why not try introducing hand feeding? People do that with hummingbirds all the time on YouTube. lol
But seriously, there's a guy that has a website out there on how to gain trust of wild birds that come to feed. I'll try to find it.
Poor budgie! Used to have a couple when I was a kid. Fun birds! We used to tape toothpicks underneath glass on a combo chair lamp/table, and when the birds were let out for play they would peck the glass and try to get the toothpick but never could. lol
When all else fails, stalk out the area with a huge net.
