Phone call with Continental rep reveals they are as confused about the policy as I am.
The consensus opinion was that I can call 24 hours before my flight (9:45 a.m. Sunday) and try to get a confirmed spot on a flight within 12 hours of my call.
He did, however, mention that the flight would need to have a seat available with the same fare code as my original seat. Is this normal with Standbys? the policy doesn't mention this.

In any case, I think I'll check seat availability on Saturday night and go to the airport Sunday morning to see if they'll let me on the 9:45 flight for $50.

Thanks for the advice.