I wanted to jump in at this point. I have struggled with the same issues and some time ago a discussion on this forum was helpful to me. The advice that worked for me is...use a sharp blade, xacto #11's. I buy them in bulk and change them often. Cut with a light touch. Don't expect to pierce 1mm of cardboard in one cut. Score a line, and on your second pass cut through. It did not sound conviencing when I read it, how would I cut in the same groove twice? As it turns out, the blade wants to follow the previous cut and it is not an issue. I have gotten very good at freehand cutting of compound curves. I agree with what was said regarding leaving the blade in the paper as one repostions the work. I couple of other things I have learned. The mat cutting surface matters. I have been using a nice big Xacto cutting mat. However I recently picked up a cheap hobbyco cutting mat. It's thinner and harder and feels cheaper, however the blade does not sink as deep into this surface and cutting is more precise. Bear with me I have two more items of advice. You can't cut what you can't see. I built a couple of Fiddlersgreen planes without maginfying glasses and the results were not good. I have spent more then I care to admit on magnifying lamps, lenses, loups and found that the best for me is a $9.00 pair of clip on to my glasses magnifying lenses. These have a focal length of about 20 inches and realy improve my whole modeling experience. And lastly, "Don't cut to the back of your hand" That's a saying I learned from my father who was an uphoslterer and cut patterns in cloth and wood every day. The point is don't attempt to cut with the material you want, obscured behind your hand. What this means for me as a right handed person is that I always cut with printed model part to the left, and the scrap to the right. The guideline is not behind the blade or under your hand.
So that is my wisdom. I am confident in it as I was very stuck with how to wrestle a nice bulkhead out of 1+mm of cardboard. So far it has worked for me. Now with 2mm board the same prinipals apply howerver it is necessary to cuss.
John