So, I clearly need to strengthen my party in order to beat these bosses. Normally, that would mean leveling up in a dungeon, and maybe buying some equipment.
Leveled up a little more, to 44. I thought my guys would have infinite stamina the night before a full moon, but both Aigis and Mitsuru became exhausted. I took that as a sign to try fighting Strega again.
Finally got Dominion, the Justice persona I've been wanting for a while. Had to level up to 42 to get him. Justice personas are dear to my heart, because Chihiro was my first and favorite level-10 commu. Dominion leveled up to 45 with the bonus XP for having a complete Justice commu. Also fused a Taraka (Hermit) and a Clotho (Fate).
Actually kinda enjoying the grind this time around. But the fluffiness of the storyline, and its disconnectedness with the rest of the game, have me longing for Persona 2's engrossing story.