I'm one of those hyperactive healers who just wanders around for the giggles, sweeps everybody whenever possible, usually from outside of any party, and I spent most of yesterday just hopping from fate to fate, gathering seals around Vesper Bay, keeping whatever tanks ran by up, and nuking the side aggro off.
The 4-position filters in the settings are great for someone like me. I swap from No filters at all, to Party, allowing only the people with me, a soloing setting blocking all but Monsters out, and a Custom one allowing all people for those times when you walk into someone else's problems.
Hit X on the guy controlling the hate so the cursor bounces back after each cast, find anyone worse off and tap X before casting and lock on there... just sweep back and forth changing your primary as needful.
Macros are good to get the heal onto the guy who has the hate at the moment, just remember to be fluid and don't get tunnel vision.