EL34,
For $175 all your homework is done for you, debugged and tested. When considering the total cost of your CNC it is a reasonable price to pay.
I also have looked into building my own PID controller, but not to save $175. It would for the design challenge since electronics was my trade - retired now.
Your hardware is basically your "brains" (arduino, micro, whatever...) via an optocoupler to a 15A triac phase control circuit. Another opto sensor for detecting the painted router shaft. From there it is mostly software of your favourite PID algorithm.
No, I don't have a detailed parts list for you. Just the concepts. This project can be educational to explore....