I read that you have already cut your new stencil so these suggestions are after the fact....However, in using the DBK plastic you have to leave more bridges (uncut sections) as it is more flexible.
Also, you have already discovered to put equal pressure on both blades. It is very easy to hold the cutter as you would a pencil and it twists around and doesn't cut.
It is a good way to enlarge and make the motif fit the space.