Spec definetly plays a big part. Your first tactic sounded like the best bet. Just have your priest focus on nothing but healing and wait a few strikes until your dps kicks in. I'm not at the house or I would post one of my videos from SFK (I ran the instance at 18 and was able to aoe farm by 22). Basically my tactic when I first go into a new instance and am undergeared/level is :

set my priest macros to nothing but healing, no dps. I use a sheep macro rotation to try and do only single targets. I let my paladin get a couple of hits in for aggro and then go all out on dps. With your priest doing nothing but healing you should have no problem staying alive, even if you have to spam heal/renew.

Once you have cleared the instance a few times and your level/gear increases, switch your priest macros to dps and healing. What I usually do is have a smite macro tied to my mage's fireball. So when i'm spamming fireball, my priest is also supporting with smite. I say to wait on this because if you are getting hit hard you do not want your priest in the middle of a cast and have to stop it and wait for the GC before you can get a heal off.

On boss fights I usually start the fight with the dps doing their longer casts. I rush in with my paladin start generating aggro and instantly start casting pyroblast and holy firex2 (soulfire for your warlocks). Because the cast timers are longer this allows me to get aggro and takes a big chunk out of the boss right away.