Just looked it up and just found the Link to it, but without any clue whose story it is. Might have confused the author, but if you say the trope sounds about right, maybe it is. https://www.angelfire.com/mn/runt/o-07_The_switch.htm I think I stumbled across it during some Google-Fu session.

The crossover one sounds like loads of fun! Might try to find it. :D