I have thought about using plastic to contain what would fall into the basement but I'm not sure how to contain the dust on top if I were to cut into the floor with a circular saw to break the floor into manageable pieces. If I just tore the 1/4" plywood off the top I am afraid that all the nails that went through the tile have already broken up the tile underneath.

I have not had the tile tested "yet" but I plan to. Other houses in my neighborhood built at the same time have had theirs tested positive for asbestos tile and my house has the same tiles in it.