If you're having downtime where the tank and raid is topped up, there's no reason not to switch over to Cleric and chuck out you DoTs/Bane as SCH or Stone/Holy as WHM (and later, Gravity as AST). As you get better with your Healing skills and also become familiar with the raid you're in you will get more confident to stance-dance and DPS while healing, which is the mark of a good healer in this game.

If you don't want to DPS and want to still do some end game content, WHM (commonly, also AST) is usually given the role to solo-heal the raid while the SCH is the one stance-dancing and doing DPS. Alex Savage Floor 1 is the primary example for this, where WHM solo heals Faust and solo heals the Oppressor pre-split. Floor 2, they usually solo heal up until wave 5/6 as well, although if every mob is stunned, they can just got to Cleric and chuck out Holy and Stones until the stun wears off on the packs and resume solo healing after the stuns wear off.

Could that be the solution you were looking for?