Yeah, I figured most Raids and Advents aren't so hard, so straight offense can work.

Guild Orders and Tower Events on the other hand, I only do well when I use Andromeda (and Solomon to nuke the first few trash mobs on tower). I keep thinking that when I get good healers, I could finally substitute Andy for Hercules or Shingen though.

As you pointed out, Medea's ability, "3-3: All allies CD reduced by 1 (8T CD)", looks good inded. More heals, more damage cuts, more buffs and debuffs, etc. If the other kamihimes in the team can provide useful skills, seems Medea is actually the best of the bunch. There is also this 10x damage nuke to all enemies with her Soul Weapon... Worth considering.