Retested Mischievous Heart earlier and now I'm pretty sure it adds +1 priority to zero base power moves.
This was my previous post about it. Everything there is confirmed.
Then I decided to test it against priority again;
Erufuun used Stun Spore!
Wild Shimama was paralyzed!
Wild Shimama used Quick Attack!
Then I tested this against a friend's scarfed Basurao (so that it was faster than my Erufuun);
Basurao used Aqua Jet!
Erufuun used Stun Spore!
Basurao was paralyzed!
The last nail in the coffin will be when I get access to an ExtremeSpeed Pokémon, which now has +2 Priority, and test it against Mischievous Heart Stun Spore. I'll also test Taunt and Substitute immediately after I get the TMs, and will start breeding for Encore Erufuun so that can be tested too.
edit; For completeness sake, also tested in a double battle:
Erufuun and Abagoora vs Zebraika and Shikijika
Erufuun: 114 speed
Abagoora: 78 speed
Erufuun used Stun Spore!
Wild Zebraika was paralyzed!
Abagoora used Aqua Jet!
Wild Zebraika fainted!