Thank you. I appreciate the direction and it does help alot.
For other people's benefit, the link to the Singapore-Australia Double Taxation Agreement effectively states that:
1. Double taxation on property
income is indeed avoidable.
2. The property income will be taxed in the country in which it is located (in my case under the Australian tax regime).
3. Choice is not available when it comes to the question of which tax regime the property income will be taxed under.
4. Negative gearing is still possible but in my case is irrelevant since I do not have any other Australian income to offset the deductions against.
I'm still chasing up the banking options but at this stage, it doesn't look too promising. None of the so-called "global" banking institutions I've approached in Sydney actually cater for the international financing services I'm looking for.
But I'lll keep trying and see if there is any better way to service a mortgage in one country while working in another. There should be, given how internationalised the workforce has become these days. Very surprising.