I don't actually alpha roll my dog, but every so often I do have to pin her down just to stop her from running around in circles after I yell at her. At first I just picked her up and send her to time out, but now she thinks I'll pick her up every time I yell at her, so she has started to run around in circles at high speed. It's very annoying.
I have taught Totoro to lay on her side on command, with head down on the floor. So when I jump on her, she lays very quietly, and doesn't struggle or act scared. I don't really know if this action is equivalent to alpha roll or not.
Sorry I don't have any insight. But if someone wants to give me suggestions on how to do a time out more efficiently, I'd be happy to get new ideas.