The multi-division league scheduler could already assign officials from the command line. It now has a box on the page. List your referees one per line, such as Ana (Hawks): Tue, Thu max 6, and every match across every division gets one, shared out evenly. Nobody works their own team's match, nobody is on two matches at the same time slot, and weekdays and match caps are respected.
Matches nobody can take are listed with the reason instead of hidden, an independent check re-reads the result, and the table and CSV gain an Official column. The box is part of the share link. Everything runs in your browser; no names are uploaded. The wiring is tested and the engine is tested, but nobody has clicked the new box in a real browser yet.