Turn,
Does your company have any j/s agreements with air carriers? Check with your Chief Pilot or Union Rep.
Next step is to call the Jumpseat hotline of whichever carriers you have agreements with and list. These are usually the non-rev travel lines, ask the Res agent about loads - you usually only get code words like, "good", or "not good", sometimes you get actual booking numbers like "110 booked, 100 capacity" (ie 10 oversold) or "37 booked, 82 available" (ie wide open).
Last, show up at the gate, in biz casual, no uni required, about 45 min prior to departure - (gate agents are never there 1 hour prior, and are busy getting ready for the first 5 min anyway) and ask for the JS. They'll probably run you on cass anyway, and discover that you're not Cockpit JS qualified, and either give you a seat in the back if the plane is wide open, or more likely ask you to have a seat, and call you just prior to departure, assuming a seat is available in the back. Don't forget to say hello to the cockpit crew, introduce yourself when they are not running a checklist, and ask for a ride - even if you've got a seat assignment. Its mildly irritating when OAL JSers failt to ask for a seat. Plus you lose a networking oportunity. One of my Captains ended up with a LOR to UPS from a JSer who asked for a ride -and it works the other way too.
Luck!