Helena has raised a subject that I was going to inquire about: predators. Do you have birds of prey in your neighborhood?I know that when we take Casper outside he is always scanning the sky for "bullying bigger birds". Maybe Mate has had a nasty experience when you weren't there to witness it.
However I am inclined to think Mate's problem might be loneliness, when he was in the house he could see and hear what the family (flock) were up to. Casper loves being in the garden as long as we are with him. A companion sounds like an excellent idea to me but I don't have the experience to suggest whether it is best to have another Galah or a different breed. If I was him I would put my selection in this order: Lady friend, Drinking buddy, a companion of a different species. But I'm not a Galah, and being Australian his first choice might be a drinking buddy*
*other racial stereotypes are available.
Its a lovely aviary but how about a bit of lawn in the bottom for him to play in/search for bugs etc. If he trashes it, just keep replacing it - he is obviously having fun.