To answer the original question, yes there are chairbacks to be found. Sometimes posters on this site list them. Just monitor the boards multiple times a day during game week if you can (this board and any others you may be members of) and more often than not you've got a good chance of finding something. Prices tend to be more reasonable via that avenue, though it requires some persistence and good timing. As others have said, Stub Hub is usually an option too although often a bit more expensive. If you are BDC member, in prior years they have made a small number of chairbacks available to the public a few days before each weekend series. Usually down the third base line. Have not heard if they plan to do that again this year.
My biggest piece of advice would be to not limit yourselves to Saturdays if you can help it. Friday nights and Sunday afternoons can be your best friend if your schedule allows it. Demand is typically not quite as high but you still have enough people going to where it's a good atmosphere.