With several of my recipes (like vanilla sponge and WASC) when I invert the cake parts of the sides fall off. Any tips? Does it ever help to cool the cake in the refrigerator before inverting?

I would suggest you explore different ways of preparing your pans for these recipes. Do you usually use shortening and flour, a spray release, or what? Probably the most foolproof way of doing this is to put parchment down and then grease the pan. Also, you might be baking your cakes too long, or at too high a temperature for that particular recipe. Another possibility is that you might have to cut back a little on the sugar in the recipe. I find that recipes that call for more sugar than most tend to have sides that separate. Unfortunately, you might have to experiment a little to find out exactly what will work. Isn't there a real expert out there who could help with this problem?