Thanks for all the replies so far! Some comments:
I have to disagree with this. It's good that they slow up taking Holy Grounds at least a little bit. They are pretty easy to overwhelm with numbers or strong units. For humans, two mages plus one or two cheap units to soak up the damage will help. Four rangers also worked for me. For orcs, try one troll and one shaman. Undead have most trouble because vampires do no damage to fire elementals. For them try a zombie to soak up damage and mass skeleton snipers maybe? Summons will also help: imps, Fervus bears and strong rats will all die against elementals, but at least they will soak damage. Oh, and like SolaceAvatar said, put elemental/spirit damage buffs on your archers/mages, that will help.
Never had issues with GFEs playing undead. I used a pair of Flying Galleuses (Gallei? Oo) to whittle them down. After a bit of xp with the proper perks (elemental resist and regen) and Regen/Elemental Resist spells (both easily acquired early in game) they dish out more to the elemental than they take. Just gotta remember to park one beside it at all times so it can't rest (a tactic I use with ships vs Sea Serpents quite a bit as well). If one gets hammered a bit you have it rest a turn to heal while the other keeps firing (being a ranged unit the GFE - and Sea Serpent - will almost always move away from your unit before attacking meaning you are clear to rest if needed while moving another adjacent to prevent him doing the same). And the advantage to using a Flying Galleus is ignoring all the trash melee mobs that might be in the vicintiy since they can't attack you and even the demons/winged serpents with range tend to be almost one-shotted by an un-upgraded/leveled Galleus.
The biggest issue I encountered battling GFEs was them kiting me into other crap (almost lost my Demonic Advisor one game because it dragged me towards a few evil trees and a second GFE - gotta love teleport to fix crap situations like that and pull back to heal up, buff some more and churn out a damage sponge unit to distract the others).