I am not certain, but I think there are a few problems with this plan. First of all, I believe you have to do US surgery training to enter subspecialty training. I don't think general surgery training in Australia will count. For example, on the Yale cardiothoracic surgery web site for which you provided the link:
To qualify for admission to the program the applicant must be eligible for examination by the American Board of Surgery, having completed a full residency in General Surgery including a final year as Chief Resident.
I don't think you can be eligible for the American Board of Surgery unless you have completed a US residency.
Also, licensure requirements are different for international graduates -- usually a year or two longer.
It is quite frustrating but I don't think there are many ways around this.