Comparing our logs on Primordius I see several things that stick out. First is that you didn't use Spirit Shell or Prayer of Mending at all. There are several lower damage parts of the encounter that you can use to stack Spirit Shell and apply a PoM on someone. I'll discuss further about Spirit Shell below. You also use a lot of Penance casts on players. Penance is your top atonement healing, and you're wasting 34% of it to overhealing on that pull. Penance will heal for more if used as a damaging ability, and it's a smart heal so overhealing will be reduced.
I would also highly recomment getting Solace & Insanity instead of Mindbender. In every fight this tier, Solace will provide more mana than Mindbender. Mindbender is good for Heroic Horridon, but that's because of the certain mechanic it has.
Regarding your thoughts on Spirit shell, you seem to be misinformed (either that, or I'm misinformed). During constant AoE periods, some people will be higher than other people. Your PoH will almost certainly overheal a couple people per cast. Spirit Shell ensures that none of the bubble is wasted to overhealing. Ideally you want to cast it before the big AoE damage comes out, but in most cases it is still better to use than PoH during constant ticking AoE damage like on Primordius. Spirit Shell also benefits from Archangel, so you should macro Archangel and Spirit Shell together. There is plenty of time on Primordius to park yourself in such a way that you can stop and cast for several seconds without getting hit by the purple pools and staying in range of the 25yard boss aoe thing.
I clearly misunderstood SS, I had thought I read somewhere that SS didn't benefit from archangel and that old bad information just stuck. I went back to crit build, did a macro to AA and SS and used it, tried to remember to keep PoM up (although sometimes it bounce 1 or 2 times and just fell off the 3rd). I worked on rotation changes in LFRs. Before I got the LFR tier chest yesterday I think the macro'd AA & SS were all above 250k bubbles (playing with dummy casting on self, unbuffed). I try to only use penance to damage the boss, but was finding I needed to sometimes give a direct heal to a player taking a lot of damage. We did the achievement kill with no one mutated, so I did what I could do with the incoming damage. Perhaps this week we'll do a normal kill, and get a chance to try something different. I wasn't using PoM on CD, but was waiting for it to bounce the 4th time or fall off a player. Should I really be using it on CD instead? I switched to Solace & Insanity, and yes, that was a nice improvement too. So, my healing has improved and you've been a great help.
edit: Should I macro in a Power Word: Shield to get barrowed time before AA and SS, so I get the first PoH off faster?
One problem with Primordius is that you need to Fully Mutate first, or else your atonement damage is going to suffer. I'm not very good at using the log browser in WoL, so if someone else wants to parse how much atonement healing was done when you weren't mutated, that might help clear up your problem (specific to Primordius).
You are exactly correct. I wasn't mutated, which hurts my atonement healing. However, the kill was the achievement kill with no one mutated, and the healing was "interesting". I tried to atonement heal as much as I could, but there were some serious "oh crap" moments, hence penance on player direct heals. We wanted to do it before the next nerf. For our 1st run as a new raid team, I think we did pretty well.
Lots to learn. Thanks to all for feedback and help!