Wow - I have never even heard of most of the trees you all mentioned! I live in Australia. I like to attract native birds and butterflies to our garden (butterflies have to be caterpillers first, remember, so some butterfly plants actually get eaten by caterpillers first!

)
We do have a problem with aggressive immigrant birds from Indonesia/Malaysia chasing away our wild birds.
I asked the local plant nursery staff this very question - how do you attract native birds to the garden and still have shade? Shade is really important to us as we live in the tropics. The nurseryman said we could never go wrong if we planted native flowering or fruiting trees. There is such a wide variety of plants to choose from, some shrub height and some many times the height of the average house. Planting natives means the native widlife would be attracted to our garden, and the immigrant wildlife would not. And we can have some lovely shady trees in the garden this way too. Two problems solved by asking one question!
So I recommend you ask your local nursery people for advice about your particular area.