You don't have to try to put something over on the unsuspecting airlines. They would rather sell their unsold seats to you at a huge discount than to have the seats fly empty. You've come to the right place. Travel agents sometimes buy up blocks of unsold seats and resell them to their clients. I'm afraid I can't help you with them yet, but I'll probably add that information soon.
Some airlines have email lists they mail their weekly specials to.
You need to be ready to travel almost immediately to take advantage of their offers. Usually they mail their notices on Tuesday or Wednesday for the following weekend. Typically you need to fly out on Friday or Saturday, and return on Sunday or Monday. I now have links to 4 of them. I'm hoping to add more as time goes on.