Fireball

You seem to be calculating something incorrectly. :)
The "Order of Unity" skill shifts the hero by 0.25 on the initiative scale, and the hero will start the battle within the range of [0.25; 0.5].
This means that the initiative range for units is [10; 20], below which a unit has no chance of going before the hero, and above which a unit will definitely go before the hero with "Order of Unity."
A unit within this range has a chance to go either before or after the hero.
Orc units, without any artifacts, fall within this range, meaning they already have a chance to go before the hero with "Order of Unity."

Furthermore, the described tactic, as seen in the example, is for the late game.
This means that many initiative-boosting artifacts will likely be collected.
This needs to be taken into account. These artifacts are not fully compensated for by anything, and the hero's initiative is not increased either.

Also, 120 leaders, 10 per week, even from a single castle, is 12 weeks.
Not 5 months, but only 3.
And yes, there could be 2 castles, or a dwelling of level 5. It will be faster.