There are very thin sawblades on the market that are typically used for cutting fret slots. Using or adapting one of these with a "micro table saw" (made for certain kinds of small project hobbies) and a precision sled for thickness stops might be a solution to create your blanks from the rod with minimal waste, but there is also that fine line around ideal blade speed that cuts without heating too much. That's always the big challenge with plastics and similar material.
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The most expensive tool is the one you buy "cheaply" and often...