I'd say based on the video your biggest problem is the amount of time where you are not casting. Most obvious in movement but also apparent at times when your casting mechanics fall apart and there is a delay between spells.
In a different regard, normal mode council isn't a very healing intensive encounter until the final phase since a lot of damage is avoidable. Some raids will two heal that encounter. In this case there is less healing to go around and the other healers are likely beating you because they are most constant with their casting.
"In anything, if you want to go from just a beginner to a pro, you need a montage." /w TankSpot WTB Montage for Raiders.