When we did butcher on HC we had 30 man and I didn't feel like I had mana problems at all. Looking at your log, the main difference between mine and your healing is the usage of FoL. I reserved FoL usage to sub 30% on boss, otherwise it's not really needed. I healed in early cataclysm aswell, when the damage/healing ratio was about the same (weak heals and "slower" damage), don't feel panicked when people drop low, try to increase your HL usage and see where it takes you is my tip. If people die, it's not really your fault, but the other healers not doing their part.
For reference:
http://i.imgur.com/jVVfKcs.png
Note this is from 30M HC and I had ~42,5k HPS. I also have the DMC trinket (stage 1) and Everburning Candle, which greatly helps me with mana.
Glyphs: Merciful Wrath, Sacrifice and Beacon (not really needed here, I don't beacon swap from tanks)
Talents:
Speed of light: Must have on this fight to rush to range stack after knockback
FoJ: this one don't matter
EF
Clemency: This one depends on your tanks, if they need CDs pick this
Sanctified Wrath: must have talent IMO in combination with merciful wrath glyph. The reasoning is that without the glyph, AW becomes
too good and it gives you more overhealing. With the glyph you still do loads of healing and you get to use it more often when healing is intense.
Prism and BoF.