As I said, I'm not wedded to exact details on how this would work, but my suggestion is that we not change the schedule because of an event that happens on the weekend. Why? Because the House of Commons has tools in place currently to deal with that. It's called emergency debate. You can petition the Speaker to recall the House in the evening to have an emergency debate. That power is used not infrequently by members. So there are already tools in place.
The second thing I note is that our system already doesn't allow for that. If an oil spill happens on a Friday at five o'clock, we have to wait two days before the House can ask questions of the government anyway. So if an oil spill happens on Saturday and the Minister of the Environment is slated to come Tuesday, that's no different from an oil spill happening on a Friday and the minister coming Monday, as is currently the case.
Many other parliaments have a once-a-week or twice-a-week rotational schedule. They are no less accountable, no less timely than in our system.