Hey, I finished the cutout in one day! Rather than thread, I used dental floss (I had read about that once). Now, the floss did not do the cutting. For that I still used the X-acto blades. However, I found two techniques aided the process. First, I used water as a lubricant. I did not want to use oil for fear of contaminating the plastic and hurting the finishing process. Water works. I guess it acts as a cooling agent- the blades did not stick as frequently. Especially the PE razor saw- I could saw for a minute or two at a time without the blade sticking.
Secondly, the dental floss cleared out the residue of the cutting. So I would cut a little, then use the floss to open up the cut. In spite of the water, I believe the plastic gets soft and sticky enough from the heat that the dust and particles stick in the groove. Once it was cleared out, the floss would stop cutting, though, so I don't think floss or thread would work well as the only cutting method. Anyway, the door opening is complete, merely smoothing up the cuts now.