Before we get started, so everyone else doesn't search like me
Armory: *
Logs: * can't even quote links
Spirit is going to be different for each person. If you feel comfortable with your mana, it's fine to drop spirit, if you don't, it's fine to add more.
Going over the logs, spell usage, in terms of percentages isn't bad, to be honest. The main issue is your CD usage and when you use them on Galakras. The add phase really requires little to no cooldown usage, so not using there isn't really an issue. However, when Galakras comes down, that should be nothing but you and your healers chaining cooldowns, one right after the other. On a lot of your wipes, I noticed that the two other healers would spike in healing, but you would remain static, suggesting you're either not using or not coordinating your CD's properly with our co-healers. For me, I generally start with casting Holy Avenger when Galakras comes down and EF blanket the raid. Once HA is over, I then pop Divine Favor and Avenging Wrath, together, and go with a Holy Radiance > Holy Radiance > Holy Shock > Eternal Flame rotation until that runs out. Once that CD is over, pop GoAK and do the same rotation (LoD if necessary if people are being stupid with their stacks, at this point). Don't forget that you have Devotion Aura, as well. I generally try to save it for when I think I can't get people up quickly enough for the next explosion, to make sure the raid lives.
Also, with regard to your talent choices for this fight, I would take Lights Hammer over Holy Prism. Generally, LH is going to be better for stacked fights while Prism is going to be better for spread fights or fights where the bosses hit box is huge (Immerseus, Norushen, Iron Juggernaut, and Malkarok, mainly). LH is especially the better choice on Galakras for 2 reasons:
1) You can use it during the add phase to not only heal tanks/melee, but also do a considerable amount of AoE damage to the adds as well
2) You're not wasting a GCD on Prism every 20 seconds when Galakras is down, when you can just drop LH and forget it while getting insane healing.
Also, I would personally take unbreakable spirit over clemency on Galakras. There isn't any real need to have 2 of any hand on this fight, but the 30 second Divine Protection and possibly multiple bubbles and 2 Lay on Hands can be raid saving (or at least self saving).
Your numbers are also probably lagging a bit behind due to gear. Both your co-healers have their legendary cloaks (but your shaman for some reason isn't using the legendary meta, what's up with that?) while you have neither, which puts you a bit behind in ilvl, and makes mana usage a bit more difficult, as well.
And on a final note, get a belt buckle