Walkthroughs for custom maps.

The question is more of a technical nature: are there any effective ways to get a stuck generation process moving? For example, I need to generate a specific creature for a week or catch a specific hero with a certain army in the tavern, but when the day transitions, in 99% of cases, only one generation occurs (disabling HD+, SoD_SP, launching the game without HD-Mod does not help). I even downloaded The Shadow of Death separately from the existing Complete edition, launched the save in it and in Era, and I can get the first unique day transition to work, but then the same sad week of groundhogs appears again.

And maybe someone knows about any programs for generating a starting save?

Here, it was discussed somewhere that the pseudo-randomness in battles is tied to the computer's internal timer, i.e., it is through the computer's time that randomness occurs. In simple terms, if we attack a gorgon with a dragon in battle, and the gorgon's gaze doesn't trigger, and it won't trigger, if we attack in the same time frame, then when we repeat the battle, we can wait 1-2 extra seconds, hit, and the gorgon's gaze will trigger. The same nonsense works with the pseudo-random casting of spells by Wizards and Genies; waiting for a pause or, conversely, quick actions often allow you to choose the desired random outcome.
Based on observations, the same principle works in battle when we move our creatures on the tactics map. If we place our forces in a strict order in an identical formation, and Wizards go first, then they will always cast the same spell (for example, blessing). As soon as we change the placement on the field or change the order in which they take turns, the spell cast changes. This was discovered through experience on Chinese maps, where Wizards or Genies must (and I mean must!) cast a specific spell in battle, for example, slow or haste. In such battles, you have to make 20-50 attempts, and you can already learn to make Genies cast the spell we need.

Regarding your question, the generation of the week on the last 7th day, at least for me, almost cannot be changed. If you roll back to the 6th day, play it, then play the 7th day, the week generation may change.
I have both the HD Complete edition installed on my computer, which I usually play, and some old Heroes 3 The Shadow of Death. When I need to change the week of creatures, I reload the saves in these different Heroes games, and the week may change, but it is almost always one of 2-3 specific options.

And lastly, on some maps, for example, the German Dunkler Horizont or one of some Chinese maps, I don't remember the name, I noticed that the author achieves the appearance of certain weeks of creatures. For example, on the Chinese map, the Devil week was constantly generated every other time. And our starting castles are Inferno! therefore, there was such a situation that if we don't upgrade Devils to Archdevils and don't buy them, then after a couple of weeks, the Devil week will appear again, and we get a huge increase! But then we fight with a large army of un-upgraded Devils. Or we upgrade and get stronger Archdevils, but our creature week will not give us an increase. That is, the author somehow managed to force the frequent generation of specific creatures - Devils - and tie this to the plot and the choice of how we will fight, with what army. And in Dunkler Horizont, it was the periodic generation of the Pegasus week, which could sometimes be recruited. So, what week will appear may be somehow recorded by the author, although I am not sure, because I only noticed this on these two maps.

If I need the desired week, then I make a save on the 6th day, play the 6th and 7th days, and then something may change. Also, the building made/not made in the castle, the dismissal/purchase of a hero may affect the generation, but this does not always help.
All this is purely my observations without any scientific basis :)