Hey Julian, What State do you live in (Vic) ? Of the species you have listed, I have used ironbarks, SG, Blackbutt, and Beech. The beech I used was Tasmanian beech, so it might not be the same as Northern Beech. Tassie stuff is nothofagus cuninghamii but I think it grows in rainforrest areas through eastern Australia, I also don't think it is a common commercial timber much anymore. It makes a nice bow though. She oaks might be worth a try if they grow near your area. I haven't tried but it is also called Australian Pine by guys in the US, and they have made good bows from it.
I'm not really a fan of our eucalypts, for bows. They will make a bow if the grain is right, but they can be fickle timbers, both in tension or compression.
Straightness of grain on the back and sides of the board, and freedom from knots or pins are what you should focus on regardless of species.
Osage grows in the eastern states, if you know where to look. Black locust, oak, elm, ash, crepe myrtle can be got from gardens via tree loppers, if you keep your eyes peeled. Native desert acacias usually make good bows and the wood can be very beautiful.
Also I you live in a major city you could try timber sellers that have imported timber, oak, ash, south Am timbers.
The bow in the photo has long levers. You might try increasing the width of the bending limb. If you haven't made many yet, focus on a bend through the handle bow before takling a more advanced design.
