You need to be able to pump out 15k HPS every once in a while. Remember, over the course of a fight that number may only be needed twice for 10 seconds each time, so your total HPS may be much much lower, especially as Discipline.
PoM is absolutely your friend, where PoH is something you don't want to be spamming unless absolutely necessary - it's an awesome tool to use when everyone in the party is getting hit lightly and the shield and HoT (if glyphed) have time to work. Also, as Disc your Divine Hymn is awesome when everyone is getting frustratingly low.
Healing Ozurk is a weird fight, but for the most part it is doable with 4kHPS or less, so your numbers most certainly aren't the problem. Understanding the fight's intricacies is what will set you apart. Disc is very good at this fight.
The Order Never Changes:
Elemental Shield will Reflect Damaging Spells back onto the caster. As soon as he does this, Shadow Word: Pain for a long lasting Debuff.
Ground Slam is a Conal AoE that targets the tank. If he/she gets hit by this, they are a goner and it is beyond your control as a healer to handle this.
Paralyze will freeze everyone in the zone for 15 seconds - if this stun lasts for its entirety, it will explode for about 50k shadow damage. If you are hit with any other damage it will break it early and avoid the damage. By SW:P yourself you effectively keep a steady DoT going that will help you break Paralyze early.
Shatter is a Point-Blank AoE for which everyone must run out. This will kill most people and severely injure the tank, so again if anyone's getting hit by this they shouldn't be.
As the healer for this fight, healing is not the priority - what is a priority is controlling the fight so that your group is able to do damage the majority of the fight and are able to avoid the damage from Paralyze and his AoEs.
To accomplish this:
SW:P quickly when he uses Elemental Bulwark
Immediately after DoTing him, use Dispel on Ozurk to remove his Elemental Bulwark so your casters can continue to do damage.
Once Paralyze takes effect, be ready to Dispel anyone else trapped by Paralyze once SW:P breaks you free. If you have 2 or more Ranged DPS, Mass Dispel is awesome here. This will allow the DPS more time to wrack up damage on the boss.
Be ready for his Elemental Bulwark for the quick DoT and Dispel, rinse and repeat.
As for Fel Reaver and High Priestess Azil, it is almost certain that it is your group that is doing something wrong and not the heals. For instance, getting nailed by a Harvest is almost certain death for anyone, including the tank. Again, Rock Throw is an instant kill, as is getting trapped between a number of gravity wells.
One thing that's tough to learn when healing is that you really can't heal through stupid somethings, and that's not meant to be sarcastic or degrading. If people aren't playing the encounter correctly, it's made to be unhealable.
Warning - Attempting to patch together any coherent message from my posts may result in chronic headaches and/or intense vomiting.