This time was made possible by decent execution and some very nice luck: In this run, the primary source of RNG (and time loss) is in the AI movements of the green player. Fortunately, at the end of the game I saw that the green player's hero was killed in the ruins. This reduced the amount of time spent waiting between turns.

With the same luck and better execution, I could see this going to 0:53 or maybe even 0:52.