I have tried both the wood-burning tool and Exacto knives, and didn't like the results either time, and find the I do better just using my sewing machine!
I don't use the really hard template plastic for this, but I mark the stencil with a sharpie, then unthread my sewing machine and using the largest needle I have, just stitch along the lines! You can do it with the feed dogs up, or drop the feed dogs and do it with free motion. Use a long stitch length so you don't just perforate the template plastic. You can also use Golden Threads paper the same way.
This video might give you some ideas:
http://www.goldenthreads.com/