A program for determining luck/morality in Heroes 3!

Or not. :) In my opinion, no army parameters generated before combat change during combat.

Yes, I checked - nothing changes anymore. :)
But while I was checking, I realized that after casting "Haste," the Centaurs' speed becomes 14, so they can easily run around the central obstacle, and no Harpy is needed at all. :)

And, undoubtedly, we can discuss everything together,

Yes, of course. By the way, there's another thing. In my fight against the Titans (in the open field), the Wizard never changed his first cast. That is, if he was in the second slot, he would definitely cast "Haste," if in the fourth slot, for example, he would always cast "Bless." But the second cast was different, sometimes there was none at all, although I'm not sure I reproduced everything exactly the same up to the second cast.
In general, the mystery of controlling Luck also interested me during the champion walkthrough. Just like you write, there were cases where it seemed I had found the correct sequence of actions for Luck to trigger (in my case) for the Sharpshooters on the second turn of the battle.
Let's say, the first time it triggers by chance while going through options. I write everything down, repeat it a second time - it triggers again. Well, I think I've got it. I repeat it a third time - and now there are different outcomes. After what you said, I'm now thinking, perhaps that famous pause is to blame?
Let's say, the first 2 times I performed the correct sequence of actions, BUT - I clicked "Shoot" a second after the turn passed to the Sharpshooters. And the third time and onwards, everything was so familiar it was automatic, and I clicked the mouse immediately when the turn started. Maybe that's why the seemingly "found" Luck suddenly disappeared?
And another conclusion. If the pause really matters, then it follows that the sequence of moves isn't important at all! With any setup, you can achieve Luck triggering (by guessing the pause), and the sequence is only needed in the sense that it's simply easier to calculate and reproduce the necessary pause for a specific turn.
In short, tests are needed. I'll try to replay my battle save, if possible.

Added after 27 minutes

It seems Mr. invisible explained the Wizard! In your example, IMHO, you shouldn't have pressed DEFEND.

Not entirely sure what invisible has to do with it:)
The discussion was about the fact that, according to Vbn, battles in "closed rooms" always have the same battle map. At least, his tests allowed for such an assumption. I gave an example that with his save, but on my machine, the battle in the Griffin Conservatory has different casts from the Wizard. To clear my conscience, I checked what would happen if I didn't stand still but moved the Sharpshooters; naturally, it was always the same. The Wizard's cast was still different.

The answer seems obvious to me. Damage is never superfluous, and Luck is Luck. As can be seen from the video, morale there only triggered on the move and without any Leadership!
But one thing is for sure, Mullich would have struggled longer in the Conservatory,

Do you think Jenova struggled little enough that later, in the video, her morale "only triggered on the move and without any Leadership!" :)
I think struggling is the last argument. For evaluation, the result is what matters first and foremost.
Regarding obviousness - damage is never superfluous, but the question is: what is better
- Shooting 3, Luck 1
- Shooting 2, Luck 2
- Shooting 1, Luck 3.
If we assume we can freely upgrade these two skills twice as we see fit, which setup is preferable?

Mullich's specialty isn't critical in the Conservatory, but in the battle against the Titans, Mullich would have helped save the Angel, but with Basic Shooting instead of Expert, the Sharpshooters' damage would be different and would likely require more turns,

After the Conservatory, Mullich would come out with Expert Shooting. He levels up to 5th there, doesn't he?