Can an elderly woman authorize me to cast the pebbles on her behalf before traveling to Saudi Arabia, or must the authorization take place in Muzdalifah, given that I might not see her there?

It is permissible to appoint an agent for the stoning (ramy) for someone who is genuinely unable to perform it, because she is allowed to appoint an agent for the entire Hajj if she is permanently unable to perform it. It is preferable for her to appoint one of her companions to witness the stoning and say "Allahu Akbar" (takbir) at that moment if possible. It is also recommended that she place the pebbles in the agent's hand so that she has a part in the stoning.