If there are no compelling reasons, ie, a sick family member that needs ongoing specialist treatment would you consider just using the Public Health System?
Other than when I worked for Multinationals who provide it as part of your package, I have never had private health insurance. We are rarely ill in this house so I view it as a waste of money. On the odd occasion I have used the public system it was of an acceptable standard. You are using the public system anyway by the sounds of it, just paying privately for it as well as in your taxes.