How we could improve priests:
Again getting ideas from SC-2. This time with the field hospitals:
In SC-2 there is a building that regenerates the shield of the units instantly (Even while fighting). But it requires energy and once it runs out, it remains inactive for a while.
https://liquipedia.net/starcraft2/Shield_Battery
The field hospital might have a similar ability to heal units during combat quickly. (How about instantaneous healing consuming 10 food and 5 gold for every 30 stamina points restored?)
Surgeons being garrisoned in hospitals could make this ability recharge faster.
The field hospitals will slowly heal units that are at rest anywhere on the map very slowly, or if they are close to it they will be able to heal faster (Even if they are moving, but without fighting).