Erm, healers using a controller should just go into their menu and under "When weapon drawn" select "Target Pets/Summons/Chocobos".

You can SS pets at the beginning of the run, makes them even more durable than they already are. Also, you don't want your fellow Scholar's fairy to die and have them waste a SC bringing it back. As for this option potentially interfering with normal targeting, I certainly hope you aren't using left/right to select heal targets >.< That's what up/down is for.

Unfortunately, healers can't immediately see what status effect your pet is under. But after running Amdapor City a few times, maybe they'll start double checking the pet. The dungeon isn't terribly hard to heal so taking some time to examine pets shouldn't cause any problems.