I have tested the process using blender version 4.9a and it works but sadly not in the latest 2.59 version. The image I have attached should give a better idea of where the cut needs to be (Red line), and just to note that the proposed plane is not flat.

The process I followed in Version 4.9 was to click once at the beginning of the cut with the knife tool and then again at the end whilst holding down the "K" key. This gave a perfectly straight line.

With the amount of texturing that the model will need when complete "Boolean" is off the list of possibles because as you state it will create "bad geometry".