There's some indication elsewhere in the board from Adam Smith that,
"I believe I was the one who pointed that out and the cow just confirmed it. But it's 2 hours before departure to cancel via the app or website. Cancellation can still be done after that, but requires human intervention from AC Reservations, Concierge, or an airport agent."
I did a mock booking and you are correct the 24 hour refundability option is indicated. However, Air Canada requires you to call in to access this so it is the same problem.
You are going to need to convince Air Canada that you actually tried to contact them within the window. They will have internal records about hold times at the relevant time. Having information about you contacting the LAX agent will help your position.