1. Play with the patch. It speeds up the process on average and negates the advantage of people with unlimited time resources. All talk about not being able to check whether the patch was installed is just a smokescreen. Upon close examination (read: top walkthroughs), you can determine whether at least everything is repeated on the patch. If so, there's essentially no crime even if the patch wasn't installed and the save is accepted. Many saves cannot be verified, just as they cannot currently be verified for other methods of cheating. Both offline and online play largely relies on an honor system.
2. The third criterion is needed because ties on the first two do occur. If someone can't be bothered to optimize, that's their personal problem. I myself rarely optimize parameters fully and don't complain. If someone loses sleep over a shortfall of one mercury, they should see a psychotherapist, otherwise they might worry themselves into trouble. Perfectionism is a useful thing, but everything in moderation.
3. Parameters should be calculated with artifacts and AFTER the battle, because that is the final "strength" of the hero.

2 DmitriyAS and Dirty Player
Apparently you have a lot of free time and a strong love for random generation. Or maybe you've just won a lot because of it compared to others and don't want to give up such a "starting bonus"? :) This brings to mind

In offline, everyone is by definition on equal footing!!!

Let's look at this issue from another angle. Suppose we introduce a so-called patch. What game would the tournament then be based on? Heroes 3? No. With the so-called patch, the battle mechanics are completely different, and therefore an honest person wouldn't dare call this game Heroes 3. In that case, come up with a name for this new game.

Now reading THIS is truly astonishing. Let's leave aside the question of why you speak for all honest people, but apparently I am not an "honest person," because I would call the game Heroes 3. After all, the game was called Heroes even with the ban (pre-fix) on double-cast, killing a grand stack, etc. And that too is GAME MECHANICS, which were changed by a ban. Moreover, the patch actually brings the battle mechanics closer to what the developers intended, while the permanent morale in round 1 has already come to be considered normal. So your words are either extreme conservatism or simple hypocrisy.