Thinking further, the concept of measuring one parameter (wire diameter) and calculating the number of turns based on that is flawed. It is an open-loop system and doesn't take a myriad of other variables into account, therefore the calculation will never be perfect. What if the next batch of forms are slightly different in size? What if the standard deviation of same changes? Etc. etc.
A better approach would be to somehow sense when the winding reaches the end of the form rather than calculate it. This is a feedback mechanism that allows for all those other variables (including the ones we haven't thought of) and doesn't require constant measurements of the input (wire). Maybe it's the angle of the wire from the supply point, or maybe tension, etc.
I can buy any number of products that are neatly wound on their spools, e.g. string, thread, wire, solder, etc. There must be some fairly common mechanism to do this that you just need to discover. The wheel has already been invented here. The question I would ask is how are all these other products wound on their spools neatly, not how can I invent an original contraption to do it.