Since people have been talking about the Advent Loyalists being relatively short on goodies, here are three new techs that would help make them more unique and powerful.
Holistic Mastery(Tier 8 Hostility): Removes the level cap for Titan and Capitals
Unity's Guidance(Tier 6 Harmony, 2-level): Increases xp gain in friendly culture by 15%-->30%
Directed Assimilation(Tier 5 Harmony): Each capital boosts culture generation in gravwell by 10%
This would serve to make Advent loyalists more focused on their capitals (a nice contrast to the Advent rebel's focus on sacrifice), and would do something to assist their struggle at pressing their cultural advantage. And unless I've missed something, they shouldn't be too potent in midgame, and by lategame, bomber spam is always present as an answer to Level 14 capitals, and having the Coronata at level 11+ would just make up for the relative weakness of its abilities.