Instead of a power swap, how about a mentality/feelings swap? As in, the characters remain themselves, keep all their powers and memories, but their basic outlook on/attitude to life, their dominant feelings get swapped with someone else's.
Say Yuuri and Sakura switch with each other. Yuuri still practices skating and loves Victor, but rather than stress over how he's not good enough and worry that Victor will lose interest in him, he goes about his day with a sunny "everything will surely be all right!" attitude. Sakura, meanwhile, has sudden bouts of anxiety and jealousy.
...This is a little hard to pull off if you're canonblind to each other's canons, but I think we're by and large pretty familiar with each other's characters to make it work. Instead of a "you swap with one character for the duration of the event" it could be more of a "you switch for a short while with whoever happens to be nearby" event.
For the record I am well aware this is just a dressed-up version of the Personality Switch Event. Rp like it's 2000.