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"but the idea is – the main hero is a strongman + two agile mages who explore the map."
This is a must. It's dangerous to split the main army into many small parts, and it's absolutely impossible to explore an XL map with just one hero; a mage can do a lot even without an army. But you need even MORE heroes – these three or four defeat and capture, while a few completely unintelligent ones pick up what can be taken without a fight, deliver reinforcements, and quietly take the slow units away from the fighters at night.
"however, if there are many teleports, the AI always beats me – please suggest a tactic with teleports – just standing in the doorway can be risky."
In each castle, don't just take two types of the slowest or most useless creatures; with the help of even a weak hero, they can usually fend off the opponent's non-main heroes.