Corella, Galah and Sulphur-crested Cockatoo. The Musk Lorikeet is one species I hoped to photograph that is missing from the list even though it does occur in this area.
Given that you will probably want to maintain a reasonable distance from the birds, it is the birds themselves
that provide the solution to the steep angle. What you are hoping to achieve is a pose that has the bird/s leaning towards you. This creates the impression that the birds are closer to eye level. This is not as difficult to achieve when you consider most parrots are curious and will peer towards you. The other bonus in this situation is that if the bird is leaning towards the photographer the chances are the eye contact and head turn will also be acceptable.
To get a decent background involves moving around to line up a tree in the distance that can provide something other than sky in the background. The further away from the distant trees the creamier the background. Fortunately at this site, which is predominately open woodland there are plenty of large trees that can be used for the background. Personally I don't think you need a solid green background, but even a partially covered background works to break-up the one dimensional blue sky.
To get what I regard as decent images of these species I've made four different visits to the site, either in the early morning or late in the afternoon. To get all the elements to work together required a lot of time and images.
Please take into account that birds should not be unnecessarily disturbed during their breeding and nesting cycles. Be prepared to back away if a bird appears to be alarmed in any way.