Insulating your roof will change the way your house acts. You have a dark, metal roof with a thin layer of "sarking" and r-3 insulation? No wonder it gets hot in summer! You have a big solar thermal collector on top of your home, with not much thermal shielding. The heat just soaks right in.
Here's a typical modern roof design:
The maker pushes wood-fiber insulation. Typical thickness of the shown section is 12 inches. Their low-u designs are even thicker. Passive house designs with pitched ceilings typically have 16-18 inches of insulation between plasterboard and the surface of the roof.
No matter what approach you take with heating and cooling, insulation will reduce your heat load if done. If done correctly and sufficiently, it will dramatically reduce your heat load. Once it's done, it doesn't cost any more and keeps on saving you energy indefinitely. If you can't do it yourself, have a pro do an energy audit for you to see how much of what will save you energy the best. This is an area where a little research up front is money well spent, and can open your eyes to why your home acts the way it does.