I have always been told my rep that although specific things are over time, time and half, or double overtime, the hour is billed only as one unit - but on the higher rate.
That is, if you went over time on one day by an hour, you will bill for that hour, but then the time, since already paid as overtime, will not be billed because it put your over the weekly hours.
You can, for example, never go over on the per day, but end up going over for the week, and then you bill for the times over the week.
Since you have to get overtime approved before it's scheduled, what are your producers saying? I think you should talk to the rep, as this is very specific issue. I think Stage Management and the producers should discuss, and make sure possibly the deputy and Biz rep should be all be included on the conversation.
Also, how you choose to bill overtime is also a personal choice for yourself, although you should bill correctly for the actors.