First let me start off by saying that the two abilities Surge of Light and Holy Concentration have completely changed the way I play a holy priest now. Because of them, the way I generaly play my holy priest is as follows.
The 6 second cooldown on CoH really did not change my play style at all. My main use for CoH is to proc Surge of Light from a critical hit on at least one of the targets. I will then use Flash Heal instantly and free on whoever needs it. Outside of SoL procs, flash heal should not be used often at all except in very select cases such as single target emergencies (like Patch), on clothies with too little health, or when the healers are not working well together. If all the healers are trying to snipe the fastest heals to top the healing meeters (like a holy priest constantly trying to get in a flash heal because thier Greater Heal takes too long), congradulations, you are in a newb guild/pug raid that does not work well together. Have fun with your huge amounts of wasted mana from overhealing and FH then go /emo on the Blizzard message boards about how your class always goes OoM.
Now, as far as when the entire raid takes huge amounts of damage, there is a GREAT undersused spell in the game, Prayer of Healing. Lets take for example, Vortex on Malygos. Before the fight I tell the other healers "don't heal my group during vortex, I can keep them all up". During the vortex I just hit PoH which then almost always procs an instant free FH (which I will use on the lowest health target or tank) then I will CoH for another free FH and then rinse and repeat until the vortex is over. I just healed 6 members of the raid with complete ease and relitively very little mana. No over healing happened from other healers because they knew that I could do the part I said I will do (I really wish I could target a raid group with PoH though). If there are two priests in the raid, even better. Put one in each group and never worry about mass raid damage again.
For single target healing, Greater Heal is where it is at. Unless your tank is loosing health faster than you can cast GH (on very rare fights or phases), you should never have to cast FH unless you have a bunch of healers trying to snipe heals from each other (the sign of poor orginization). GH has the added benifit of a Surge of Light and/or Holy Concentration proc on crits allowing for some extra manaless heals. Crit is just AMAZING on holy priests now. GH until it crits, then possibly three free heals in a row (SoL gives a free FH, HC gives a free FH or GH) then throw in a meditation for some serious out of 5 second mana returns (making spirit way more important than MP5 these days).
Note the lack of CoH spam healing mentioned in these very basic holy priest tactics. The only place I really miss the spamming of CoH is on fights like Alextraza where you have to always be on the run (no time to stop and cast).