Tyler
We play all year round at my club in Adelaide. We aerify heavily in mid-spring. End of October for us. Hopefully, the bent is running by then, so a quickish heal over 2 to 3 weeks.
We have also aerified at the very start of autumn, again to try to get coverage by bent whilst it is still active. This year we used slightly narrower, deeper tines. Less removal of material than spring. Because of a drought, our last recovery was slow.
This year, we are undertaking the same heavy spring aeration, followed by multiple mini-tynes through summer/autumn. No major autumn aeration this year, similar to your proposal. We'll see how we go. We have had far better greens through winter with the full aeration, but have had to give up three weeks in our prime playing time (early autumn) to do so. Hopefully, we'll get good autumn and winter surfaces this year.
James B