Probably the easiest way to do what you want to do is to make your halftone on the computer from a scanned neg, as smithdoor suggests, then print out an enlarged neg on inkjet transparency film and use that to contact print on your photoresist material. A window screen is much too coarse for this--halftone screens were on the order of 150 (low newspaper resolution) to twice that or more for books.
I don't know what you're expecting, but probably getting the high end of that will be a losing battle, and you'll be lucky to make the low end work right. I messed with halftone offset printing in the 70s, and it was real twitchy. I took a class, and that helped. There was a lot to know, and I don't know where you'd get that info these days. Your best bet is to find someone who's actually doing it, today.
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