HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

I have never played Heroes online and I have never played chess with a timer.
However, I am well aware of the charm of chess clocks. When time saved on quick moves can be spent on critical, long moves. The only thing is, if they are ticking during battles, then time should be added for each battle, I believe.

actually, chasing golems with ballistas is not a violation of the rules and why would someone set further restrictions for me, even if, say, I'm not picking my nose while the timer is ticking! maybe I'll have to pay for cans too and hives just purely found a can, visited it and minus 100 more?

This can be solved by adding time proportional to the number of moves in battle, i.e., adding for every move in battle. That would be very correct, imho. Only here one needs to find the right ranges for additions. Starting time + time per map move + time per battle move.

In general, why fear chess clocks? Uncheck the chess timer in Advanced Options and you play with a SoD timer.