For Cutter's Cry and Aurum Vale in particular...

Learn to love Regen, and make a habit out of refreshing Stoneskin between pulls (or when the last enemy is about to die). These two will extend the time you can stick around in Cleric Stance for a good while.

For Cutter's Cry, I hope you've been keeping your Esuna button healthy. Second boss and onwards has a fair amount of debuffs to remove, especially if the party plays poorly on the last boss in there. Paralysis is a bitch to deal with if left unattended, and Heavy will make it all the harder to dodge future AoEs. You might also be expected to kite adds on the first boss; simply Regen the tank and yourself, maybe a Cure (II) to solidify threat, and then Sprint in circles around the edges of the room while the rest burn the boss.

For Aurum Vale, there's nothing particularly interesting going on there healing-wise, though it does give you a chance to showcase how amazing Holy is (depending on how shoddy the AoE available to your DPS is). There's lots of stuff that needs to die quickly to prevent unnecessary pain, such as the seeds on the final boss. Otherwise, roll Regen on the group to counteract various DoTs and have fun cursing the melee who can't dodge 100 Tonze Swing (and Esuna'ing the noobs who can't dodge Glower or Eye of the Beholder). :P