>>>>The hope would be that I would get on a flight that was NEARLY zero availability, not already at zero, and have a chance at a bump. I realize if it's zero that means there is no space available (give me a little credit here!).

I've had mixed experience trying to get onto flights that don't have the class of service available I've booked in. I've found the elite line to clearly push to keep re-books off of flights that are fuller than others. If it is starting to look potentially full down the road, the resistance can be very stiff. Sometimes an agent will contact a supervisor to ask approval, but if there are any more-wide-open options available you can expect to be put on that one with little choice. If most everything is pretty full, your only other option might be to cancel the whole itinerary for a refund without penalty. I don't think you have any obligation to call to rebook within any particular time frame, but your options if you wait too long might be exceedingly limited.