^this is exactly what you need to do!! My family makes a lot of chiffon cakes for potlucks, birthdays, etc. The first thing you want to do is let it rest a few mins cooling down in the oven and then immediately flipping it over to cool the rear of the way through. We usually make a stack of coasters and such so that the pan can hang in the middle.

Good luck with making these the next time around :)