First off, the difficulties you are having are due in large part to your material. Birch plywood can have voids, glue pockets and knots that will adversely affect your cuts. Even when something works for one area of the board, it may not work on another section.
That being said, if you set your thickness to be different than the actual thickness, you are taking the laser out of focus. For precise cuts, a deforcused laser is not the answer.
There are quite a few posts about cutting 1/4" birch plywood if you utilize the search function. Here is one thread with visuals of the results: 1/4" Baltic birch plywood cut test