My father was a pilot so I'm used to this - we flew staff travel alot. All you can do is play the game.
a) Pick routes that are quiet. If we were going to Europe in the European summer, we'd fly to the US and then go from the US to London rather than try and go straight to Europe.
b) Pick the times no one else wants to fly at. A lot of people don't like to fly during the day because they can't sleep on the plane. Therefore it's usually not as busy.
c) Have a back up plan. Be prepared for the situation whereby you may not get on the plane. Have backup tickets in the event that you're flying through a hub. For instance, if we were flying back from LA to Sydney, we would get a ticket for the sector LA-Sydney flight and one for the LA-Auckland-Sydney flight (with QANTAS you were allowed to cash in the vouchers/tickets you didn't use).
d) Dress nice, be polite to the staff. The staff who work those desk are usually bitter that you're going somewhere and they aren't. They have the power. Smile, be nice, flatter them. They'll remember.