Self insure is a bit missleading with most lenders. The lenders you've mentioned don't actually 'self insure', but they have their own packaging agreements with the major mortgage insurers.
This means that within certain parameters, they can set their own policies. Outside of these parameters the application is still forwarded to their insuer.
As an example, Westpac will forward an application for over $750k with a 95%LVR the their insurer, who I think is PMI. Below $750k the deal is simply packaged and the insurer underwrites it without looking at the individual applications.
Examples of lenders who really do self insure would be La Trobe or Liberty. The have a 'risk fee' instead of LMI (which costs about the same), but there's no insurer involved at all.
If you describe what you're planning, it might be easier to give you more specific guidance.