I agree a lot with what Jynus says, even though s/he and I don't see completely eye to eye on Spirit
I was going to say the same thing - your usage of Healing Tide Totem is low. In a seven minute fight, it should be used twice, maybe three times. You're correct in thinking that you should use it when people have taken damage, but you have to realize that Blizzard balanced our hps around it. So...if you don't use it, you're bound to be low. The same is true with Ascendance.
I would love to use the glyph of Totemic Recall, but I'm not consistent in recalling so I'd rather use the water shield glyph. However, if you take a look on the Elitistjerks Resto Shama Guide, there's a table that indicates which fights the WS glyph will be beneficial and which aren't. Not all the fights does it come out as a mana gain.
Looking at your logs, I noticed that your mana back on Water Shield was only 8k. Surely, it dropped off. That seems extremely low even if it's not glyphed. I was just curious if you have something to monitor your WS buff.
Like Jynus said, I wouldn't recommend Unleashed Fury for this fight. I only use that talent when my assignment is a tank and they're taking a ton of damage.
Someone mentioned something about not being afraid to overheal. They obviously didn't look that closely at your logs, since your overheal is over 50% for the kill. I think as you get more comfortable with the fight, it'll be easier to be strategic about what healing spells to use.
Great job on the healing stream usage. That's something I need to work on!
EDIT: Sure enough, I looked up the Ta'yak fight and that is one that needs the WS glyph on. That explains why the mana back is so low on those attempts.