Printing specialized halftone screens used to be part of Illustrator's tools, but has gone to the wayside. I wonder why you do not have the screen printer output the films themselves rather than rely on you to do it? Do they charge extra for that? Another possibility is to find a local print vendor who can output film and have them do it. You are getting frustrated because of the limitations of the application and its output capabilities or lack thereof. Ideally, you'd need a high res printer capable of printing halftone screens via a specialized RIP.
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