I am in a similar situation. If you trade the ASX with an Australian trading account,eg E Trade Commsec etc,you must lodge a return with the ATO.
As a non resident you are not eligible for the tax free threshold,aprox. $5,0000. So in effect you must pay 5k extra in tax every year.
As a non resident you don`t have to pay the medicare levy.
Australian address wont give you resident status,however having an investment property in Aus will.
If you set up a trading account in another country you must abide by there tax laws. In my region places like Malaysia have no CGT. I would personally rather my cash stayed on Oz soil,so i am in the process now of obtaining an investment property.