The late start is the duration of OR shift that is not used at the beginning of the shift. Basically it's the difference between the shift start time and the first patient entry time.
I think that I can find :
the first patient entry time by putting a milestone in the process flow.
I think your outline sounds like a valid solution. Another solution instead of the milestone would be to have some trigger on the OR that shows when they change state from "Idle" to "Busy" or another state. I think either way would work the way you want.
