I'm probably starting to sound like a broken record at this point, but redesign Healers (and maybe Tanks) to have cyclical self rewarding gameplay.

Casting heals builds dps buttons, casting dps builds heal buttons. It will promote healers to play the way they do at high level content from get-go.

There could even be potential catchup mechanics built in to cover situation where you manage to triage through insane situation and your heals/shields get full-ish non-overheal value by giving you access to powerful party buff or something as reward.