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

Would it be acceptable if loading a save, including an autosave, added 2 minutes?
1 minute for loading and 1 minute for refreshing memory and preparing for actions.

Or perhaps add a fraction of the time taken for a turn?

Is it possible for the timer to start ticking after a save is loaded, following a specific, useful tactical action, such as after building something, manipulating troops and artifacts, moving a hero, dismissing a hero, or trading at the market? In this case, the status quo would be maintained: you can remember what you were doing, and time doesn't pass.