Have been having similar problems on the healing side of the fence and have been contemplating going DPS. I just don't seem to be able to put out the numbers that I need to for normals and it isn't very fun. As my Druid or Paladin I am putting out 13 - 17k hps over the course of a fight depending on movement. Apparently I am supposed to be at 20k without running out of mana. That seems impossible to me at this point. I had to step down from a Normal group I cleared the first 4 with but couldn't maintain over 14k hps on Twin Ogron because of the movement.
What ilvl are you supposed to be to do Normal level raids? I am high 630s and I figured that would be enough as getting ~5 more ilvls of LFR gear doesn't seem like it would bump my numbers by the amount necessary. I do still rock a 621 mace which I can't get a replacement for the life of me, perhaps that is it. But again, I am not sure
The moral of the story is I don't really like how faceroll healing LFR / Heroics is and how I cannot seem to transition to normal level raids.
On the bright side, my DK got an epic 645 weapon follower quest. This means that the character I play least is still ahead of the curve on gearing via followers vs. the two I LFR with.