Tate, I imagine that many starting down the sharpening-from-scratch road believe that the teeth need to conform exactly to the lines on the paper, and if they do not then all the teeth will end up misaligned.
Just get the teeth as close as you can (to the line on the paper), and do not worry about the spacing at this stage. It is early days. As you continue to file, you can (and will) move the position of the tooth by taking a little more off the front or the back of a tooth. There is quite a bit of filing to do when you begin with a toothless or near-toothless plate, so there is quite a bit of time to move the teeth into the desired spacing. We are talking under a mm here much of the time, so the tooth count, per se, does not itself change.
This method takes more time, which means more patience for the amateur (like myself). But you will get there. No fancy equipment needed, unless you are making many saw plates regularly.
Regards from Perth
Derek