A rotation is easy to design for the normal week and the normal week is not the problem. The problem is the week with a deadline, a virus, and a trip, when the schedule is wrong for everybody at once.
Rigid rotations break; loose ones dissolve
Enforce the rotation strictly through a bad week and people either resent it or abandon it. Let it slide with no accounting and it quietly reverts to the historical default, which is one person doing most of it while everybody believes it is shared.
Skip explicitly, balance over a month
The workable middle is a visible skip and a longer accounting period. Somebody says they cannot this week, the system routes around them, and the balance evens out over the month rather than the week. Nothing is lost, nobody negotiates in the moment, and the record shows what actually happened.
The point is not that everyone does exactly a quarter. It is that nobody has to argue about whether they did.