Player rating for offline Heroes 3 tournaments!

Just implement this rule and be done with it! That's exactly what we're all saying...

Yes, I remember, I remember, a voice crying in the wilderness :) We barely managed to get Best of Best to run on at least two difficulty levels, though we wanted it on five. Then someone always comes along and says, "But I love playing on Normal. This rule is bad :)" Newcomers will appear, and suddenly it's too hard for them to play on Impossible right away. And then they get hit with such a rule. They might not like that. That's why the organizers will almost certainly reserve the right to maneuver with difficulty levels. But the rating will be calculated as written, and the players can figure out for themselves that they need to learn faster and move to Impossible, where the coefficient is prettier :D Otherwise, no one is going to rack their brains over balance just to bring the rating of lower league players to a common denominator with those trying to play in the higher league. Instead, there is freedom of choice :D

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And why can't this rating be applied to tournaments for other versions of the game?

Why can't it? You have to reach an agreement with the organizers. And find a volunteer who will do the counting by tracking ALL tournaments on the resource.

I believe we should go all the way. In the "Van Cunningham" tournament, if it actually takes place, I think this parameter can be used as well. This rating can be used both for individual versions and for the tournament as a whole (but in this case, aging should be removed, as not everyone will participate in all versions).

Aging cannot be removed. We've already discussed that one tournament can be skipped without consequences. And that is effectively a month at minimum.
I simply don't have time to delve into the system of running other tournaments or figure out all the tournaments. I still need to learn how to play myself.
Therefore, you can take these formulas and calculate the rating for the Van Cunningham tournament there—by the way, who is that? But it will not be linked in any way to the ratings of tournaments from VDV_forever. Or is he the one running this tournament?
Here's the thing: if all the organizers on this resource agree to calculate ratings using one system, let's say for the third version, then it could be agreed not to age a player's rating when calculating it in other tournaments for the third version, provided they participate at least once a month with at least one of the organizers of third-version tournaments on this resource. Furthermore, we could expand this: if they participate in at least one tournament of any version of Heroes on this resource, the rating doesn't age in the other tournaments.
But this requires very good communication, organization, and synchronization of tournaments, as well as a complete database of who played where and when. Otherwise, I think you'll get confused about who played where, who is playing, or who isn't, and the ratings will be a total mess :) And who will track and manage all of this?
Let's start slowly with VDV. Then, if it works out, we'll gradually connect other tournaments, but only after agreements and discussions between the other tournament organizer and VDV.

And in parallel, use the system with grails. We will get two different parameters, one of which will reflect exclusively the skill of speed-playing, and the second—the general level across various parameters.

Speed-playing skill for which version? No one will have time to play all of them.
Even playing every other one is a pain. Then rating aging will kick in. Either someone has to track that the player played somewhere. A general coordinator and strict accounting are needed—who will take this on? In other words, after every tournament, organizers must provide all information to the coordinator in a timely manner in the form of a participant list with their rating for that tournament and the start and end date of the tournament. And the coordinator will have to process all this information and provide the current player ratings list on time. So that a player entering another tournament already has an updated current rating. And this list must be available to all tournament organizers at any moment with the freshest information.

That's roughly how the organization should be. And it's not simple. Especially getting everyone to agree.