This is also something that I experience quite often, Though I’ve learned to live with it if it means a very moist cake.
I ALWAYS take my cakes out of the oven, let them cool for a bit, the securely wrap them in plastic wrap (pan and all) to keep the moisture in, and put them in the fridge until they’re cool, sometimes even overnight (a tip I picked up from Colette Peters). If you have difficulty flipping them out of the pan after they’ve been in the fridge, briefly move the cake pan bottom over one of the burners of your stove and try again.
Rather than flipping the cake onto your hand, try flipping it onto a wire cooling rack, then again so that it is right side up. There’s less of a surface on the wire rack and not as much cake will come off of the top.