Magic dealing damage based on attack? It's true that melee spells (outside of Death's which are quite strong) don't seem to compete well with alternatives such as fireballs. This would give them a better home. I would throw Burning Hands into the pot.
Gentle Rain and Mantle of the Ocean are both very powerful, so switching them would have few balance issues. (Their flavor is also similar, so that's not an issue either.) It's true that Gentle Rain seems out of place, off among abilities that all improve hero combat effectiveness. It's also very general purpose and any mage could want it. I'd say the switch is sensible.
Can you obtain a three essence tile next to a forest? I've never seen it. That said, I've found that prioritizing essence in fortress creation really cuts into production. Perhaps, with the importance of stacks of death, it's worth it... I would try to reduce the effectiveness of death stacks, rather than reducing maximum unit power level. To do so, I would implement strategic ZoC within owned territory. I would train the AI to "intelligently" deploy its army to prevent the movement of troops too powerful to fight. (IE to stack trash in the way, thus preventing advancement.)
Also, I would modify the computer's basic methodology by which it judges unit strength. Instead of trying to weigh stats, abilities and the like, it should just surreptitiously run a few battles. (I'm not sure if everyone's computer could handle this, but I do notice that many times the computer gives ratings that just make no sense. Like medium strength stacks that, even on autopilot, can handle deadly stacks.)
I see a lot of talk about horses. I find that I don't use horses often, because I can't afford the time to research them. I agree that, when I do research horses I generally switch to a cavalry only army, which is a little silly. Historically, horses actually have no real disadvantage, once they reach the battlefield. Pikemen, and other anti cavalry defenses rarely were able to go beyond negating advantages. However, horses, like all animals, were a pain for the supply line, and ate through a nation's wealth. Also, there was rarely sufficient availability to outfit entire armies. As such, if a change to horses (and wargs) is desired I propose a high upkeep cost and a higher production cost (or lower horse output.). Doing this, it would be nice to make horse tech somewhat more desire-able, so I would move +1 army size from siege weapons to warg riding. In turn, I would move rations from craftsmanship to siege weapons and first aid kit from war colleges to craftsmanship. This does still leave all heroes on horses- that's kind of reasonable (mounts just feel heroic) but it would be nice if there were something like 2 additional extra quest mounts.
I do think spears are too strong, but wish to argue that damage should be reduced instead of armor piercing. The weapons aren't infinitely distinct as is. Also, swords are too weak. Axes seem mostly correct.