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As a strictly offline player, I am nevertheless very concerned about the problem of cheating (I periodically read your "after-action reports"), and I would like to make some suggestions. Their feasibility varies from realistic to nearly fantastical, but let's discuss them!
Combating cheating requires both technical and organizational measures.
Among the technical measures, the following are required: transitioning to the 3rd version of the HD mod with password-protected saves; it would be even better to password-protect the random maps themselves, and even more: it would be good to save tournament maps and saves in some new format whose structure is kept secret. Along the way, it would be good to develop (perhaps as an add-on to the HD mod) tools for conducting online games to replace the existing Hamachi and others—tools that work reliably, are easy to set up, do not conflict with other software, etc.
Organizational measures will face, first and foremost, the conservatism of the majority of players who react hostilely to any innovations. In that case, we could avoid changing the existing rules and instead, for example, create a Fair Play League, in which all games would be conducted under new rules.
What new rules do I mean? First of all, the League should be led by players known in the heroes' world as honest and incorruptible. Initially, every new player joining the League must complete 2-3 random maps in single-player mode based on the same templates used for online games, and provide the judging committee with saves and a Walkthrough description for review. Why? First and foremost, as someone correctly noted, every player has something called a playstyle. It is quite individual, like handwriting. Once the style is known in general terms, it is not difficult to see which actions a player takes according to a practiced scheme and which actions "deviate" from that scheme. These actions raise questions and suspicions and must be closely studied. Thus, after every game, saves should be provided to the judging committee or posted for public view, and players must write reports about the game as soon as possible, from which the train of thought should be clear: why they went there and not here, why they took or didn't take a certain object, fought a certain monster, etc. The judging committee must (and others may, if they wish) study the saves and reports, ask questions about unclear points, and deliver a verdict: whether the game was "clean" or not. And players are obliged to answer all questions without delay!
Next is the most important part: a trust rating for players is necessary, built specifically on the basis of past games and their analysis. After all, the main trouble is that proving cheating took place is practically impossible (except for the most blatant methods)! Therefore, relations here must be built on the principle of trust: whether the judges trust this result or not. If time and again a player's actions find no clear, convincing explanation, it can be assumed that something is fishy. I think players, for the most part, still value their reputation.
The following consideration is also linked to playstyle: one must play in such a way that their actions are sufficiently "transparent" and do not arouse suspicions of "dirty" play. The player themselves must understand what will look suspicious and must avoid such actions. It's not that difficult: if, for example, the main hero walked straight north for 10 days and then suddenly turned sharply west, this must be explained by what happened that day or what they saw in front of them. Explanations of the level "I decided to take a risk and I got lucky" should not be taken seriously. How many times must a player be "fairy-tale lucky" before everyone realizes they are simply "pulling their leg"?! The reason for every action must be visible! If this consideration is not made a rule—it's better not to play online at all!
Additionally, some method must be devised to make it difficult for exposed cheaters to re-register under a new nickname. Let a combination of personal data be used to identify the person: e-mail + ICQ + Skype + IP address (or range of addresses if it is dynamic) + mobile phone number + ... Creating a new mailbox is quick and easy, but changing all of the above together, if you aren't James Bond, is not so simple!
Actually, a suggestion just occurred to me that could eliminate 99% of cheating cases online! I understand that this will cause a storm of indignation and many will demand I be burned at the stake for blasphemy, but for the sake of victory over cheating, I dare to propose it. We need to remake the way random objects are generated so that the contents of all of them—from chests to dragon Utopias—are formed not at the start of the game, but at the exact moment they are taken, and the random number for this would be set by the system timer so that the randomness is completely unpredictable. Then maphack would become almost pointless, as no one could predict in advance what would drop in a Utopia: Angel Wings or Legion Boots. Of course, for offline, such a generation method is unsuitable, as it would instead increase the inequality of tournament participants and lead to players restarting the opening of every chest 20 times...
And a few more thoughts regarding the Dimension Door:
1. Why, if it is forbidden to dig up the Grail before visiting all obelisks, is it permitted to "jump" into the dark? These jumps in themselves are damn suspicious.
2. In general, why is Dimension Door not banned in online play? After all, obtaining it almost guarantees victory! I would ban it, but leave Fly, as Fly is only possible over already explored terrain. Or perhaps Fly should be banned as well. After all, these spells allow flying over any obstacles, monsters, and enemy heroes without fighting them!