Looks like you have got plenty of US issued cardsThe US offers keep getting better and better. Chase has just upped its sign-up bonus on the Ink cards from 110K UR to 115K UR when referring from friends/family. Can be converted 1:1 to Hyatt, British Airways, Air Canada, Singapore, etc etc. All for ~$AUD276 (ie $0.0024/pt) stemming from the 3% FTF.
A new card can be safely attained every 3 months if your spend allows. Delivered in a few days by courier to your door in Australia.
Nothing in Australia comes even close. God bless America('s banking system).