An alternative that could simplify the process would be for written notice to be simply submitted to the Speaker to at least alert the chair that there is a question of privilege to be raised. The time frame need not be as lengthy as three hours; it could be significantly reduced, depending on how this committee feels about that proposition.
Par contre, on pourrait proposer simplement que le sénateur informe par écrit le Président que la question de privilège sera soulevée, et ce délai de trois heures pourrait être considérablement réduit si le comité est d'accord.