Using mass heal is the way to go where if you don't have quicken it pretty much sucks from my experience. Healing for the dragon fight is actually the easy part where quicken makes zero significant difference. The only part that can be unnecessarily mana intensive is if the groups are having trouble or lagging on setting up the genies/pillars.
Certainly the OP shouldn't have been excluded from a group for not having quicken...and I can never remember being asked if I have quicken on my fs as a way to determine if I can come or not.