A full-random setup is suitable for restoring balance, but it's unlikely to be effective in determining the stronger player.

I looked at your personal stats and understood why you don't want random castle selection. Indeed, with virtually no experience playing several castles, it's quite difficult to expect success. But you yourself are talking about a "stronger player," and one of the criteria for strength is the ability to play any castle (and on any template as well). We have a player who played (I don't know about now) almost exclusively Jebus and only Castle. But he didn't really aim for victories in tournaments. There's the "Favorites" tournament; there, everyone is protected from randomness. Everywhere has its own rules, and they are the same for all participants, so you shouldn't change the rules but learn to use them to your advantage.

And the AI has no motivation to win if it doesn't affect its position in the group.

This is a rather strange argument... What about the AI's motivation then? The tournament was offered to you not to show how cool the AI is. We are all ready to analyze your game, offer advice, explain our actions, and answer any questions. This is the main goal. Skill hardly improves in games against equally matched opponents.